Continuity mistake: Right after Paul goes home with the doctor, the doctor and his wife are clearing the dinner table talking about Paul staying at the house. The wife turns to the dinner table and is holding 2 napkins. The camera angle changes and the wife is now seen walking 2 glasses over to the sink.
Continuity mistake: In the chase sequence where Paul Vitti and Dr. Ben Sobel are being chased in Sobel's Grand Cherokee, we see the car plow head-on through a bank's drive-thru ATM machine. Yet later on when we see a shot of the car's front grille again, and the car doesn't have any front end damage from the crash.
Continuity mistake: In the scene where Billy Crystal and Robert De Niro are eating at a Sushi Bar with a crew of people, Billy Crystal is acting up due to a reaction of medication and alcohol. Robert De Niro threatens Billy by telling him that he would stick a f***ing fork in his eye; when De Niro is waving the fork around you can plainly see a noodle on Billy Crystal's face, however, when the shot changes a second later, and shows Billy Crystal and Robert De Niro, there is nothing on Billy Crystal's face; the noodle has disappeared.
Plot hole: In the armored car robbery scene, we see the guys hoist the car over a barricade with a crane, then nonchalantly open the driver's door of the truck to get the driver and co-driver out. Armored cars' driver's doors can only be released from inside the cab, by the driver with an electric lock, unless the person has a key for the door. If the driver was halfway doing his job, they would have had a much tougher time getting in, not to mention the fact that the driver is also armed, and the majority of armored cars also have shotguns in the cab. Since none of the gang had a key for the driver's door, the easiest thing for the driver to do would be to just sit there and either wait for help or drive away. The cargo area of the truck is also bulletproof and not accessible from the cab. The drivers could have simply let them take the gold if they didn't want to get involved, and not risk injury or death by opening the cab doors.