While it can be difficult, it is not physically impossible to hold on to a person when a parachute is released while skydiving. Skydivers often do this for fun, with the passenger leaping away from the carrier, and activating his own parachute. This is known within the skydiving community as a "Mr. Bill" skydive.
Near the beginning of the film, one of the Angels jumps into the car on the pier and it is at an angle facing wooden pylons. When she hits the accelerator the car takes off in a straight line down the pier.
When Natalie throws the muffin at Dylan in the office, it punches a hole in the door and sticks there at a perfectly horizontal angle. A moment later, when Bosley steps through the door, the muffin has: changed color, become lopsided and is now sticking farther out of the door than it was when it hit. Also, the damage done to the door when the Muffin hit is totally different than the damage shown to the door when Bosley steps in.
When Alex first sees the Thin Man, Alex and Dylan are both wearing shoulderless and sleeveless dresses. As they chase him down the stairs ripping off items of clothing to prepare to fight, Alex ends up in a bodysuit complete with sleeves and shoulders.
When the Angels are chasing the Thin Man through the stairwell at Corwin's party, Alex is wearing a red strapless shirt. When they emerge at the bottom of the stairs, Alex is wearing a long-sleeved black jacket.
When the Angels are first fighting the Thin Man in the alley and Natalie kicks him under the chin causing him to backflip, you can see the padding on the back of his jacket which is needed after the other two Angels then kick him into the chain link gate.
During the race car scene, the Angels are at the California Speedway in Fontana, California. A few seconds later, the chase leads them to San Pedro, California, 70 miles away, where the Vincent Thomas Bridge is visible.
At the exotic dance club, Director #1 clearly is holding his beer bottle by his fingertips, and not touching it with his pinkie; Dylan's scanning device shows a full hand-print including his palm. Director #1 holds the beer bottle with his right hand; Dylan uses the fingerprint "glove" on her left hand. A sophisticated gel scanner would be able to distinguish the difference in the sequence and location of the fingerprints; a left handed print of the right-hand fingerprints would not work.
When Dylan has escaped being shot through a window she comes to a house where two boys are playing video games. The game (Final Fantasy VIII) is a one player game, but they are playing with two controllers.
A retinal scan is a scan of the inside of the eye, not the visible external part. At Director #2's house, the device clearly scans the Director's iris. The contacts that are made from this would only disguise Natalie's iris, not her retina. A sophisticated retinal scanner would distinguish the location of the retinal image as well as the image itself; an external contact would not work.
When Knox shows Dylan the picture of his father in the army, we see him with his arms in the air and the other man covering his face next to him. When they close in on the man's name, there are fingers near his name tag, which weren't there in the larger scope of the picture. This is to show the tricks memory can play.
While attempting to rescue Bosley, Natalie receives a phone call and says it's from Pete, before answering. The next shot shows Pete talking to her from a pay phone. Perhaps Natalie recognizes this particular payphone number, or Pete used a phone card with a number of his own.
In the beginning of the movie, Jason takes a bite of Alex' muffins, and simply acts like they taste terrible. Yet when Alex brings the muffins to Dylan and Nat, the muffins are as hard as rocks. There must have been a passage of time.
When Natalie is getting out of the Red Star mainframe room, it is shown that she is somersaulting and exiting while the door is closing. In the next shot when the door closes fully Natalie has simply disappeared. It would be impossible for her to get out of the airless chamber in such a short time gap.
There is a common misconception that USA law requires actors portraying military personnel to wear the uniform improperly ("out of uniform") so as to not be "impersonating" military personnel. This is simply not so. 10 U.S.C. 772(f) does authorize the wear of an armed forces uniform by an actor in a theatrical or motion picture production "if that portrayal does not tend to discredit that armed force." SCHACHT v. UNITED STATES was a Supreme Court case in 1970 which found the preceding quote unconstitutional. As such, actors may wear the uniform in a theatrical or motion picture production without fear that it must reflect well on the military. Short version: Any movies which depict improperly worn uniforms can't use this excuse. They simply goofed up.
When the angels are all talking to Vivian Wood and Eric Knox in the "umbrella" lunch area, Vivian's sunglasses show an obvious white background, when the real background behind the Angels is clouded skies and more buildings/umbrellas.
While the Nokia Communicator cell phone rings, there is the name "CHARLIE" displayed on the LCD screen. But, instead of giving the owner an option to accept or reject the call, the display reads "Detail" and "Exit". This proves no one is calling - someone is just browsing the phone's memory.
After Jason's trailer gets riddled with bullets he and Alex are standing outside with the western backdrop in the background. Most of the bullet holes have the sharp edges coming outwards, but the shooters were shooting toward the backdrop, so that side of the trailer should have had the holes going inward.
Iroquois helicopters use mechanical linkages for the flight controls. Nor do any of the wires related to the electrical functions of the cyclic stick go anywhere near the cargohook area. Even if they did, ripping the wires out would not have any impact on the ability of the pilot to fly the aircraft. At worst, he would not be able to fire any more missile, release the cargo hook, fire the cablecut device for the hoist (if fitted), or use the push-to-talk switch (the red trigger on the front of the cyclic stick that many other films incorrectly use to fire weapons) to activate the radios.
The goof items below may give away important plot points.
When Knox shoots at Dylan and she goes through the window, the shards of the glass not only change shape when she's hanging from the sheet, but the glass itself changes form entirely. When she's sent through the window, it's made of tempered glass (shatters into pebble like pieces) yet when the sheet was hanging from the spike of glass, it was a non-tempered kind.
When Natalie and Vivian are fighting, you can see the small of Vivian's back a couple of times, indicating that she is wearing a two-piece suit (trousers and a top). However, after she rips off her jacket after she and Natalie roll down the stairs, she is wearing a one-piece garment (catsuit).
At the end scene on the beach, there is a shot of Charlie walking off to the left along the beach. The setting sun is reflected in the sea behind him. In the next shot (looking squarely out to sea, with Bosley and the angels in the foreground) the sun is high and to the right of the camera.
In the slow motion replay of Dylan being shot at, Knox's dialogue does not match his original actions. The first time, he puts the gun to his head before he begins to speak. In the replay, he begins to speak well before he takes the gun from Vivian. This is to show different perspectives of the same scene.