Continuity mistake: In the end of the diner scene Jude Law fires after the car with Sullivan and his son. A bullet goes through the rear window but not through the windshield. We see the bullet path go by Tom Hanks' head. Regardless, there's no bullet hole anywhere in the car afterwards.
Suggested correction: There is a bullet hole in the rear view glass.
Factual error: In the scene when Mike Sullivan is shown sitting in his classroom, the American Flag behind him has 50 stars, which it wouldn't have in the 30's.
Suggested correction: The spacing of the stars tells me it is a 48-star flag. Hard to see because it is hanging in a fold. The one where he is writing on the board is definitely 48. They probably used the same flag.
Continuity mistake: When Michael is sent to go get Rooney's suitcoat, he isn't allowed to get it, and when he appears downstairs just after coming from the study, Rooney is speaking, with his suitcoat on. Rooney didn't have time to get it.
Suggested correction: Mr. Rooney had a jacket on when he asks the boys if they brought the dice. Then, the next scene, they are in the basement shooting the dice and there is a jacket hanging next to him. So, the one in his study may be a different one.
Suggested correction: The scene where Mr. Rooney has his jacket on isn't immediately after the scene where Michael goes for the jacket because Connor, who stayed in the study, is also in the crowd listening to his Dad. And it isn't even the same jacket because when Mr Rooney asks Michael if he brought the dice he has his jacket on. And when they are shooting dice, it is hanging on something right next to him.
Continuity mistake: In the scene where Michael Jr. is riding home on his bicycle (before his mother and brother get shot) he drops his bike and runs to the house. A few minutes later when Tom Hanks is driving off with Michael Jr., it shows his bike. The bike has snow covered on it, but it is not snowing, the snow has stopped.
Suggested correction: It looks as though the bike is splattered with snow from the car's tyres.
Continuity mistake: When Jude Law is first talking to Tom Hanks in the diner, he orders a cup of coffee. They talk for about 30 seconds with the camera going back and forth between Hanks and Law. In one shot, there's nothing on Jude's table, then in the next shot of him he has a cup of coffee in front of him.
Suggested correction: If you listen carefully when the camera is on Tom Hanks, you can hear the sound of the cup and saucer being put on the table.
I was actually going to enter this. I agree with the original mistake. You do hear the clink of the cup being put down, but everything happens just a little too fast. We don't hear the waitress approaching, the camera is off Jude Law for no more than 2 seconds. When it comes back to him, the coffee is placed, and he is pouring sugar in and stirring.