Factual errors: Reverend Duncan says that the school's Bible class is being renamed "Ethics" due to requirements of church/state separation; however, it is clearly a private school, not subject to church-state issues.
Plot holes: After Pappass has been "caught" (in some unspecified way) for smashing a bicycle store window and stealing a bicycle from the display, and been fired from his job for doing this, he still has the bicycle.
Anachronisms: When Tom and Pappas are in the cab as Tom is heading for the airport in 1973, there are at least two current model cars in the background.
Crew or equipment visible: As Tom and Pappas are in the cab crossing the bridge, a crewmember can be seen in the car immediately behind them waving to the other drivers to begin passing as the take begins.
Miscellaneous: When adult Tommy's wife and son arrive in New York from Paris, their cab pulls up to his hotel. Tommy greets them with hugs and kisses as the cab driver pulls away without unloading any luggage and without getting paid.
Continuity: When Lady/Bernadette throws the mirror, a piece of the mirror cuts Tommy in the face. In the next scene when Tommy is running down the street, the cut isn't there.
Continuity: When Tommy picks up his mother's cigarettes out of the toilet, one of them very obviously breaks in half. Yet a few shots later, they are all unbroken and normal.
Audio/visual unsynchronized: At the beginning of the school dance scene, there is a kid screaming "Sabbath. Sabbath." Later on, the same kid is shown to be the DJ, and when he is changing records, you can hear his voice still screaming "Sabbath. Sabbath." in the background, even though he is not saying it.
Continuity: During the scene where Tommy throws pages of his Bible out the window, you can see a kid laughing (The one who yelled "Sabbath"), and in the next shot, he is laughing again.
Anachronisms: The Citigroup Center building is visible even though it was constructed 1974-1977.
Anachronisms: After Tom is rejected by the doorman at Melissa's apartment, a current black E-class Mercedes Benz is visible to the right on 5th Avenue.
Anachronisms: Both Trump World Tower and 100 UN Plaza are visible in the 1973 New York City skyline. They were not finished until 2001 and 1986 respectively.
Anachronisms: When Tommy is in the shower preparing to shave he has his mom's pink disposable razor at the ready. Disposable razors didn't make it to the US market until 1976, the pink ladies version not until later. (The film takes place some time during the Nixon administration '69-'74)
Continuity: When Tommy's wife and son arrive in New York, the son speaks English with an American accent, despite having been born and raised in Paris.