S.H.I.E.L.D. Quinjets flying at night are shown with red navigation lights on each wingtip. There should be a green light on the right (starboard) wing, and a red one on the left (port) wing. These are known as Right-of-Way lights, and follow the same rules that were established for watercraft in the mid-1800s.
When Thor takes Loki from the jet being flown by Black Widow, Tony Stark leaps out after them, already in full Iron Man armor. It takes several seconds for Captain America to put on his parachute and dive after him. By that time, the jet would have been several miles away. Tony had no problem catching up to Thor because of his rockets. Captain America, however, has no rockets, so there's no way he would have landed anywhere near Thor and Loki.
In the vision sequence when Loki projects himself to The Other, The Other says "The Chitauri grow restless" and his face is seen unmoving. When speaking his next line in the same shot, his face is clearly animated.
When the helicarrier starts to go down, Nick Fury tells Iron Man, "Stark, we're losing altitude," and display inside Iron Man's faceplate is counting down from about 15,000 feet. A few minutes later when Fury glances at a display on the bridge, it is counting down from 18,000 feet.
During the final battle, Iron Man explodes a "Leviathan" - one of the big Chitauri monsters - from the inside, labeling his attack 'Jonah-style'. He falls and hits a cab, which stops him. The camera angle then changes, and the cab is nowhere to be seen.
After Captain America stops Iron Man and Thor from fighting, Thor knocks Iron Man behind him a good distance before hitting Cap's shield. But when the dust settles not only does Iron Man wake up pretty much next to Cap, he is also in front of Thor somehow.
When Capt. America is in the gym punching the second bag, the bag has no tape around the middle. When he and Fury begin talking, a close up of the bag has duct tape around the center. Next it switches back to clean again.
In the closing sequence in the shwarma restaurant, Thor is sitting among the heroes, although he left with Loki earlier. If this scene were to have occurred before his departure, a pouting Loki should have been evident, as there is no reasonable way Thor would have left Loki unattended on Midgard.
The number of soldiers accompanying Hawkeye during his attack on the Helicarrier is inconsistent. We see 7 soldiers with Hawkeye when they enter through the grate on the deck, however we see a total of 8 during the subsequent scenes. 2 are killed by Nick Fury and 1 by Maria Hill in the initial shooting on the bridge. We then see another 3 at the damaged engine fighting Captain America (he knocks one out and throws another off the ship - the final one is knocked out by Iron Man). Another soldier is shot by Fury in a subsequent bridge scene and finally the 8th is subdued by Coulson in the detention area.
In the very beginning of the movie, when Black Widow is being interrogated, she has bracelets on her right hand. When she is fighting the guys her bracelets keep moving from the right to the left and finally back to the right hand.
After Loki shoots down the aircraft containing Hawkeye, the Black Widow, and Captain America, the three Avengers are standing near the wreckage, looking up at the invasion of the Chitauri, which is just beginning. A group of extras is seen fleeing the area in the background. Several minutes later, the same group of extras is seen running past the Avengers - again.
When Nick Fury is talking to Steve Rogers in the gym we see Steve from in front removing the bandage from his right hand, when the scene cuts to Steve from behind he is removing the bandage from his left hand, when it cuts back to the front view he is removing the right hand bandage again.
The plane with Captain Rogers and Agent Phil Coulson lands on the carrier you see a crew member in an orange shirt directing the plane on where to land, he is close to the plane, when the shot changes to an overhead shot he is not near the plane.
Hawkeye shoots an explosive arrow at the helicarrier and damages it. During the explosion, the helicarrier remains visible as if it didn't have its cloak on but another scene shows the helicarrier decloaking due to the damage.
Agent Phil comes to the Stark Tower to meet Tony. Pepper hands him her glass of champagne. During Pepper's conversation with Agent Phil, he holds the glass by the bowl, but in one shot he is holding it by the stem.
When the Helicarrier is attacked and Bruce Banner and Black Widow are thrown out of the lab, a wrist watch with a black band can be seen on Banner's wrist. By the time he growls, "Your Life!" at Black widow, as he starts to change into the Hulk, the watch has disappeared. And no watch is visible on the metal flooring when he crawls/scrabbles away from her.
The reception scene said to take place in Stuttgart, Germany, was clearly filmed in the U.S. (Cleveland, in fact) There are no such skyscraper buildings in Stuttgart as seen in the background. All S-Class Mercedeses shown are U.S.-spec-models, easily recognizable by the yellow front side marker lights. Furthermore, Königstrasse is mainly a shopping street, and Königstrasse 22, in particular, is a shopping arcade containing, among a dozen shops, two cinemas. There is no building in the vicinity higher than half a dozen floors, and Königstrasse 22 opens on the street, not on a square. Furthermore, Stuttgart has no elevated trains, which can be seen in the background of the square scene.
In the very beginning of the movie, when Black Widow is being interrogated, the exterior shots shows a billboard with supposed Russian writing. However, the actual writing makes no sense and is just a collection of random Cyrillic letters. Additionally, the locomotives of the train seen passing by are all new American mainline freight locomotives, and would never be used in Russia or Eastern Europe in general.
When the computer locates the Tesseract's location while the Avengers are arguing with Nick Fury, the computer displays the location with Latitude & Longitude coordinates that doesn't conform to the format it's displayed in. "LAT:45°66.12 'N /LON:76°87.32'W" is shown, the format is degrees & minutes. The minutes must be between 1 to 59, here we can see 66.12 and 87.32 are greater than 59 and not a valid way to display minutes in this format. If input as a correct degree/minute display of 45.6612 N 76.8732 W the location is actually on a country road just northwest of Ottawa, Ontario, Canada and not New York City.
The German police cars shown in the Stuttgart-scene have yellow light bars. In reality all German emergency vehicles have blue flashing lights. Yellow flashing lights are generally used as a warning signal, i.e. for roadside assistance, construction machinery or garbage trucks.
Many of the S.H.I.E.L.D. agents aim their M4 carbines by sticking the buttstock of their carbine under their armpit. No trained law enforcement or military personnel would ever do this in combat. They would actually shoulder their rifles, which provides better stability and makes the weapon's optical sights properly line up with their eyes.
In the gym the punch-bags are swinging by a chain from the ceiling, but after Steve Rogers punches the first bag off it, the remaining piece of chain is suddenly hanging motionless, which is physically impossible.
Several times in the movie, inhabitants of Asgard are called "Asgardians." While this could be excused as ignorance, Loki should surely know the correct term, "Aesir," and Thor should surely corrected its use when he heard it.
In the end-credits scene, the Shawarma restaurant is indicated by signs, t-shirts, and a chalkboard with shawarma, kabob and vegetarian specials listed. However, the back-lit menu at the top clearly shows steak, sandwiches, soups, Thai chicken salad (among others) and onion rings, and no indication of shawarma, gyros or other middle eastern/Mediterranean fare.
Where the little girl in Kolkata searches for Dr. Banner, the Bangla signboards have typographical errors: 'Chemist' was written in Bangla like 'ka-me-sit', 'Watch Service' appeared as 'ghardir da-o-kan. Even 'Centre' was partially seen to be written as 'ka-ne...'.
This most possibly occurred due to transliteration from english to Bangla unicode.
During the fight between Natasha Romanoff and Georgi Luchkov (Jerzy Skolimowski) Luchkov's hair changes length and whiteness between shots revealing an obvious stunt double in place of Skolimowski during the more physically-demanding shots.
The goof item below may give away important plot points.
When Iron Man takes the nuke through the wormhole, we see the wormhole is directly above Stark Tower. As he falls back through, he should have still been directly above the Tower. Instead, he seems to be falling closer to the rest of the Avengers, who are located several city blocks away (as evidenced by the Hulk being able to jump almost straight up to catch him, and the others running over within seconds).