Continuity mistake: During the bear in the cabin scene, after Chet puts the door back up, shortly after, you'll see the door is on the floor while Roman is fighting the bear with the oar from the steps. (Also, note in that same shot, you'll see the bookshelf was destroyed to pieces with its books all over the floor. That scene was never shown and must have been cut from the movie).
Continuity mistake: When Akeem and Semmi get their apartment, the landlord says that the room has only one window facing a brick wall. But when Akeem is out on the fire escape, he yells out to a street, not a wall. And there are two windows.
Plot hole: At the end of the film Mardukas reveals that he has been wearing a body belt packed with cash - "in the neighbourhood of three hundred thousand dollars" - ever since Jack detained him in New York. Are we to assume that Jack Walsh, an experienced, hard-bitten ex-police officer, now a bounty hunter who routinely chases down violent and armed bail absconders who would kill him without a second thought, didn't even perform a perfunctory search of Mardukas when he detained him? This man used to work for the Mafia! What if he was carrying a weapon? A body belt with three hundred one thousand dollar bills in it would be uncovered by even the most casual pat down.
Plot hole: Shortly after the robbery, Kevin Kline and Jamie Lee Curtis get together in a little flat and Kline calls the police from a landline to tell them who committed the robbery. In England this would immediately lead the police to the flat from which the call was made, and the person reporting the robbery would be the first person the police would want to find and speak to. Otto has handed it to them on a plate. (00:12:29)
Other mistake: When Brian takes a picture of his friend Doug on the boat, the picture shows Doug in a different position than that of when the picture was taken. (01:21:30)
Continuity mistake: When the terrorists launch the rocket at the RV, they break the same window of the building twice. (01:11:55)
Revealing mistake: After Jim's horse is shot from under him while running down the really steep hill, and Jim later regains consciousness, before he turns and finds his horse dead, if you watch closely you can see the horse still breathing.
Continuity mistake: During the horse and buggy ride to the church through downtown New York, when one of the girls is holding the reins by herself, you can tell there is a person under a red blanket at her feet (I guess to protect her while filming in case something goes wrong,) and only a moment later, the same blanket is black.
Continuity mistake: In a bus scene Crash is shown holding a guitar talking about being in the majors. In one scene he's just holding the guitar, the next he has a pair of sunglasses in his hand while holding the guitar. The next scene the sunglasses are gone. A couple of shots later the guitar is sitting in the seat next to him. When Laloosh challenges Crash to a fight, he's holding the guitar again.
Continuity mistake: There is a scene where the kids are being chased in a speedboat, while mortars are being launched at them from behind. One shot is of the young boy looking at an incoming mortar over his right shoulder, yelling "Look Out!", and then seeing the mortar hit on the left side of the boat.
Continuity mistake: In the scene in the restaurant where Tom Cruise and Dustin Hoffman are trying to order breakfast, Hoffman's character fixes the salt and pepper shaker a certain way. In the next shot they are opposite the way he fixed them. Then in the next shot they are back to the way he had fixed them. (00:37:15)
Continuity mistake: In the final final fight scene, Jean Claude's hair is dry and combed, then wet and sweaty, then back to dry so on and so forth.