Continuity mistake: After the song "Tomorrow" Bugsy and Blousey are in the cafe. Blousey has a drink and it has two straws and one spoon. The spoon keeps disappearing.
Continuity mistake: In the scene where the man has DeNiro pull over to the curb and says he is going to kill his wife with a .44 gun, there is a close up of the meter clicking over to $2.75. In the next shot from the backseat, the meter reads $0.65.
Suggested correction: The reason for that is because after Travis stopped the car, he turned off the meter. Then Scorcese's character asks what he's doing, and to put the meter back on. The $.65 indicates "$.65 first 1/6 mile" as clearly painted on the cab.
As the text of the original mistake stated, there is a close-up of the meter. A biiig one, that follows by quite a few seconds the meter being turned off. You can see the 0.65 before that close-up, you can see it after, it then changes to 0.75 and so on. This correction is totally wrong and the original post is correct.
Continuity mistake: In the scene where the German and Jewish drivers are arguing, there is a corner establishment visible in the background with a sign that reads "wash." In certain shots, a "going out of business" sign is visible in the storefront, while in other shots, with close-ups of two passers-by observing the argument, the same corner establishment is visible without the "going out of business" sign.
Continuity mistake: At the start of the fight in the club, the stain on Clouseau's jacket (from the accident with the parrot) is visible. Partway through the fight it has faded significantly. By the end of the fight it has gone. (00:45:00)
Continuity mistake: When the soldier demonstrates the bazooka on a truck, the projectile hits the front of the truck, but the explosion comes from near the back of the truck.
Continuity mistake: When Richard Pryor is ramming the police cars after saying "demolition derby", as the shot changes he is not wearing any glasses then he's wearing sunglasses, next shot no glasses, then sunglasses again, then back to none.
Continuity mistake: Right at the end when the man takes his mask off, a strand of blonde hair hangs out from the back of "his" head. In the next shot the hair is dark brown.
Continuity mistake: In the scene where Napolean has saved the girl's life in the cell blocks, they go back into the main part of the police station and Napolean holds the door to the cells closed. The first time you see him holding the door closed there are bullet holes above his head but there has been no gunfire and he does not act as if the people behind the door are shooting at him. It's not until the film cuts back to him a second time (or possibly the third) that there is gunfire on the sound track, the bullet holes are focused on and his character ducks down whilst complaining that he can't hold the door for much longer.
Continuity mistake: The movie opens with a gang of thieves taking the luggage of several Japanese tourists distracted by a guy pretending to defecate on the lawn. One of the robbers is snatching a bright red suitcase in the first shot, which turns into a plain brown suitcase in the next. Also in this second shot one of the bags is lying on the street, while in the previous they were all on the sidewalk. (00:02:40)
Continuity mistake: When Brooke Shields yells "Mommy said that you had to come home right this instant", there's a long lock of hair in front of her left shoulder, which disappears at the cut. (00:06:20)