Although filmmakers supposedly removed all antennae from the buildings in the Cairo scenes, one is visible (although out of focus) over Indy's left shoulder as he has his first conversation with Sallah. They appear in the alleyways in Cairo as well.
The Erma/Volmer machine pistol - the submachine gun used in several places in the film - is the MP-40 (Machine Pistol, model of 1940); the handguns used by the Germans are the P-38 (Pistol, model of 1938), neither of which was in use in 1936.
When Indy's ship is boarded by the crew of the German U-boat, the U-boat's conning tower reads "26". U-26 was a type IA submarine, commissioned in 1936. The hull is incorrect for that submarine and that class. The hull is actually the Type VIIC model of U-96 from Das Boot; however the Type VIIC came into service in 1940 during the Second World War.
When Indy and Marion travel from Nepal to Egypt, super-imposed over the map showing their route, is a Douglas DC-3. The DC-3 first flew on 17 December, 1935. The first aircraft of this type were delivered to American Airline during 1936. KLM Royal Dutch Airline also received their first DC-3 in that year, and from August 1937 used it on their Amsterdam-Batavia (now Jakarta)-Sydney route, replacing earlier Fokker aircraft. The majority of all the 300 to 400 DC-3 airframes built before World War II were in fact flying for American, Eastern, United, and TWA airlines within the U.S., and it would have been very unlikely to find one flying between Nepal and Egypt in late 1936.
The uniforms worn by the German soldiers are the tropical models, intended for use by the Deutsches Afrika Korps (DAK), and not introduced until 1940. In 1936, they would have worn either the standard wool uniforms, or, more likely given the hot weather, model 33 cotton work uniforms.
When Indy ambushes Nazis in the mountain pass on the island, he is uses what it is a modified Chinese Type 56 copy of the RPG-2 - Soviet-made shoulder-fired rocket launcher. Anti-tank rocket launchers weren't even being developed at the story's time line of 1936.
During the flight from Nepal, "Jordan" is written on the map. In 1936, the country was known as Transjordan; it did not become Jordan until 1949. Also, the shape is wrong. Transjordan in fact did not extend all the way south to the Red Sea coast but only to the northern tip of the Gulf of Aqaba, as does modern-day Jordan.
Indy's secondary pistol, a Browning Hi-Power, is a model made by Inglis of Canada. While the Hi-Power was designed in 1925 and began production in 1935, Inglis did not begin production of the Hi-Power until 1944.
After Indy and Sallah have discovered the Ark within the Well of the Souls, they pack it in a crate and it is hauled out by the workers. As it is being lifted up, Indy says, "Alright, take it up. Easy!" yet his lips don't move, and, anyway, he looks down, away from the crate and therefore can't critique the job of the workers.
Before the airplane fight, Gobler addresses Dietrich in German as "Herr Major", indicating Dietrich's rank equivalent to Major. After the airplane fight, his voice has changed (see above unsynchronized goof), and he changes Dietrich's rank to "Oberst" (equivalent to Colonel).
If the idol is made of pure gold, and the bag (which is to be a substitute) contains sand, it is way too light. Gold is about 10 times heavier than sand, thus the bag had to have 10 times more volume than the idol. Thus, Indy's trick doesn't work and the boulder falls down.
During the gunfight in Marion's bar, when Indiana ducks behind a corner, it appears that the type of pistol he is shooting changes with every cut. This is because one shot of Indy shooting the semi-auto appears out of sequence. After his revolver is out of ammo and he reaches for his holster, the semi-auto reappears and Indy keeps it for the rest of the scene. Evidently the semi-auto is his backup weapon; it appears later on the Bantu Wind.
The staff is supposed to be 60 inches tall (6 kadams = 72 inches, minus 1 kadam). The pole that Indy inserts into the hole in the map room towers over his head, indicating (incorrectly) that Indy is less than five feet tall. The laserdisc edition disproves any claim that he's standing on a lower step.
When the slab is removed from the roof of the Well of Souls, we can see that it fits into a network of supports. When the ceiling is shown from below we should see a cross pattern of supports as well as the slabs, however we only see the slabs. There is no interior support for the slabs.
In the scene on Mr. Katanga's ship, Indy points to his forehead, identifying it to Marion as a part of his body without pain and therefore kissable. Marion reaches for his hat with her left hand. After the cut, she is removing his hat with her right hand.
When Indy speaks to the government men in the lecture hall, he places his large book on the table. One of the two straps holding it closed is undone. When he takes the book to show them a picture of the Ark, both straps are again closed.
The students in Indy's lecture hall change positions in various shots. The student with the apple, seen coming down the far aisle when the lecture ends, is clearly sitting in the middle of the front row earlier in the scene. The girl who has written on her eyelids is in the middle of the room when Indy first sees her but in the row by the windows later.
When Indy is at home packing his suitcase, he is wearing a robe with a dark red collar and cuffs with some sort of stitched pattern. In the shot from above his shoulder where he pulls the gun out of the cloth, the collar and cuffs of the robe are quite different. They are a brighter red and they seem to be smooth with no stitched pattern. In the following shot where he throws the gun, he is back in the original robe.
When Toht grabs the red-hot medallion, his fingers are burned. Later in the movie, the burns on are all squarely in the center of his palm, and upside down compared to the position in which he palmed the medallion.
When the Flying Wing begins to turn in a circle, Marion shoots the Germans arriving by truck. Then the Flying Wing clips off the top of one of the gas truck's tanks spilling gasoline toward the aforementioned, eliminated Germans. We then cut to Indy struggling with the muscle-bound German, and then to Marion shooting at some other gas tanks causing them to explode. In the wide shot that immediately follows, the gas truck's tank has not yet been clipped by the Flying Wing.
Indy drives the truck into Omar's, driving through a traffic circle clear of debris. The German car wheels in; the vendors crowd in to distract the Nazis; and a watermelon is grabbed, thrown, and smashed into the ground on the passenger side of the car. When the car pulls away, however, the remnants of the watermelon are on the ground on the driver's side of the car.
When Indiana is in the map room he takes out his journal when looking at the symbols on the ground. When he takes the journal out there is a pencil in the binding, but when he closes it, the pencil is gone.
Indiana's bag during the fight scene with the bald German at the flying wing. When he gets hit for the first time the bag is in front of him. When he falls on his back side, Indiana's bag is at his side. When he gets back up the bag has returned to his front.
After Marion talks to Indy at the bar, she is seen drinking and looking at medallion. The chain goes from around her neck in one shot to dangling onto the table in the next shot without her removing it.
In the Chachapoyan temple, as Indy is breaking through the wall of spider webs, tarantulas can be seen on his back. As he and Satipo move through the boulder chute, his back is clear. In the next shot, when Satipo finally notices the tarantulas, the men appear to be just inside the web wall again.
In the classroom scene, Indy writes the word "NEOLITHIC" on the chalkboard. Later in that scene, it is apparent that the word has been rewritten (most likely due to multiple takes). The letter "H" has more curve, and the extraneous mark above it has been removed. The line under the word, once straight, now curves, and no longer intersects the bottom of some letters as before.
After the Nazi U-Boat arrives in the Submarine pen, we see a Nazi flag hanging from overhead sliding rafters and the Swastika on that flag is at the dead center, yet in the very next shot of the sliding rafters from another angle, we see the flag hanging from the same rafters, but yet the Swastika on the flag is off center, slightly to the right.
In the classroom, the male student who gives Indy the apple is clearly seated in the front row. As class is dismissed, he is in the third row, by the windows, wearing a suit jacket. And when he gives the apple to Indy, the jacket is now draped over his arm.
During the market scene in Cairo, Marion has her back to the camera when she hides in the basket. A few seconds later, when she's trying to shake the monkey off the lid of the basket, she is facing the camera.
When Indy is pointing a bazooka at the ark, Belloq grabs a machine gun from one of the German soldiers, with his left hand on the trigger. In the next shot, it is his right hand on the trigger, before immediately switching back to the trigger being in his left hand again.
When Indy and Marion exit the Well of Souls, an unidentified man is clearly seen lying against the rock face but is missing a few moments later during a medium shot that shows the same exit - the wheels of the "Flying Wing" are in the foreground. (A deleted fight scene shows Indy knocking out the man after escaping from the Well of Souls.)
Indy chases the men carrying the basket through some narrow streets, and ends up at a truck near a T junction. The different camera angles from the ensuing gunfight make it clear that the truck cannot go straight, since there is a row of buildings directly in its path. However, after Indy shoots the driver, the buildings 'suddenly disappear', and the truck explodes in a wide open square that wasn't there before.
When Indy and the monkey are getting drunk after the truck carrying Marion has been blown up, a young man in a T-shirt and jeans walks past in the background on the left side of the screen (all the other people are wearing robes).
During the shot in the plane cockpit where Marion shouts "Indy!", you can see on the right side of the window, the reflections of various crew members and their vehicles of which would not be in the year 1936.
There are many flaws with the U-boat sequence. The class of boat is wrong - U-26 was a Type IA, but that shown is a Type VIIC (this is because the film reused the replica of U-96 from Das Boot (1981)). Neither the Type IA nor VIIC - nor any of the principal classes - would have been capable of carrying the Ark, due to limited storage space and access hatches that were too small. The Captain clearly orders the U-boat to dive ("Tauchen"); however, a lack of a constant air supply, much reduced speed and limited capacity for the electric motor batteries meant that U-boats only submerged for defense, attack or in heavy weather - none of these apply here. Nor did U-boats sound a 'diving' klaxon. A cut scene shows Indy hiding aboard the boat by clinging to the periscope. However, as explained the boat would not in reality have dived, and even when it did it would not have run at a sufficiently shallow 'periscope depth' the whole time. On the surface, at least four men would have been on watch at all times. Even if he could have remained hidden while the submarine remained above water he would have died from exposure. The trip would have taken many days to reach its target and he would have died of thirst long before then. Thus, however Indy tried to smuggle himself aboard the boat, he would have either been spotted or drowned.
In 1936, Egypt was not under British rule but there was a British military presence, primarily to guard the Suez Canal. It would've been impossible for German troops to operate there without the express permission of the Egyptian government or indeed the British government, e. g. to force Egyptians to work on the excavation site. For the same reason, there was no need for the US government to send Indy to stop the Nazis' search for the Ark. Simply asking their 'cousins' to end the excavation would've done the trick.
Indy flies from San Francisco to Nepal on-board a Short Solent Mark III which makes stopovers at Honolulu (Hawaii), Wake Island, Manila (Philippines) and finally arriving at Nepal (possibly Kathmandu). All of these non-stop flight stretches (which range from 2300-3000 miles) are way too long for the Short Solent's maximum range of approximately 1800 miles.
Indy flies from Nepal to Cairo on-board a Douglas DC-3 which makes stopovers at Karachi (Pakistan - part of India in 1936), Baghdad (Iraq) and finally arriving in Cairo. With the exception of the Baghdad-Cairo stretch (about 800 miles), all of these flight stretches (which range from 1200-1500 miles) are way too long for the DC-3's maximum range of approximately 1000 miles.
Marcus Brody mentions that "The Bible speaks of the Ark leveling mountains and laying waste to entire regions. An army which carries the Ark before it... is invincible." Nowhere in the Bible does it say the Ark itself has any power whatsoever, let alone making a human army invincible. If anything, in 1 Samuel 4, it tells how the Hebrews brought the Ark into battle with them, thinking it would give them victory. Instead, they were soundly defeated and the Ark was captured by their enemies.
In the beginning of the film, the city of Tanis in Egypt is described as having been destroyed in a sandstorm and recently discovered by the Nazis. In reality, the city was probably abandoned when its water supply was silted in. Archaeological digs had been conducted at the site beginning in the 1800s, so the location of Tanis was well-known within the archaeology community in 1936.
During the truck chase, the heads of the approaching German soldiers are level with the top of the truck. Just as Indy looks into his side mirror, they crouch down, so their position in the mirrors is correct.
While tradition has it that only ritually pure members of Jewish priestly families were able to even touch the Ark, let alone carry it, nobody is seen touching it directly (except when it's opened); it's either carried on poles while covered with cloth or inside a packing crate.
The map sequence to the Island that the U-boat is traveling to shows that it is part of Greece, however the Germans did not invade Greece until 1941. The movie takes place five years before that. However, the movie references the classic "secret underground base" used in many stories in the 1930s, where the ownership of the territory occupied by the base was irrelevant.
The flying wing aircraft is more akin to the Junkers G 38 that came out in the late 1920's till WWII. Especially look at the landing gear, general shape and appearance. It was a flying wing based on Prof. Junkers own patent that predate Jack Northrup's theories that the Horton Brothers used for their Ho 229.
In the Cairo diner, Belloq refers to a watch as "worthless, $10 from a local vendor." However, while $10 in 1936 had the spending power of $164 in 2012, Belloq was comparing it to ancient artifacts worth millions.
Toht would need more than the imprint in his hand to replicate an approximate of the amulet. He would need to know the dimensions and properties of the crystal, including the cuttings on the surface, otherwise it would not refract and focus a beam of sunlight on exactly the right place (assuming he had the correct length of the staff). Since they were digging in the wrong spot anyway, having an incorrect approximate of the amulet would further give them an incorrect location.
The Golden Gate Bridge is shown; which was not completed until May, 1937, a year after the movie takes place. The Bridge itself began construction in 1933 (three years prior to the movie date), but not open to the driving public until April 1937, so it is easily feasible that the bridge could appear close to completion from a distance (as shown in the shot) even though it wasn't finished yet.
German soldiers fall from the truck (which is traveling forward at 40 mph) and roll backward - in violation of physics. When you jump from a moving vehicle you actually roll in the direction the vehicle was moving.
During the fight in the marketplace, one Egyptian accidentally stabs another near a vendor's stall, and fruit is seen on the end of the sword after it runs through the Egyptian's back. You can see when the sword is withdrawn, that the fruit is actually held up by a stick which is dropped in the background.
When Marion is shooting at the German soldiers from the gunner's seat in the German plane, the bullets clearly hit the ground at the soldiers' feet, yet they react as if they have sustained hits above the waist.
Immediately after the truck chase, Indy pulls into a market square and the peasants help him thwart the Nazis. In this scene, the character of Toht, sitting in the passenger seat of a Mercedes, can be seen in the wide shot played by the actor, Ronald Lacey. But in close-up, it appears as if his hat is just propped up on top of his coat as though the actor was not available, and no stand-in could be found; so they just propped his costume up in the seat and hoped nobody would notice.
When Toht is menacing Marion with the hot poker from the fire, one of the Sherpa henchmen is clearly wearing prosthetic makeup around his eyes, presumably to make the Western actor's rounded eyes look more Asian in appearance.
As the Ark is being packed away as a government top secret, it is shown to have an iron bar and padlock on the outside of the crate. When the crate is being pushed to its storage area, no bars or locks can be seen.