When Tommy picks his mother's cigarettes out of the toilet, one of them very obviously breaks in half, but a few shots later, none are broken.
In the butcher shop about 12 minutes in, a sign reads "Ground chuck, 39 cents a pound." Right after, when Pappas and Tommy arrive at the old lady's apartment, they tell her it's 69 cents per pound, and give her that total. Since Tommy immediately handed her back the $10 she accidentally tipped him with instead of a $1, obviously they weren't trying to scam her.
While Tommy throws pages of his Bible out the window, and in the next shot, the kid who yelled "Sabbath, Sabbath" can be see laughing.
The amount of shaving cream on Tommy's left ear when his mom walks in on him in the shower changes between camera shots.
Reverend Duncan says that the school's Bible class is being renamed "Ethics" due to requirements of church/state separation, although a private school like this one would not be subject to church/state issues. This statement is meant to introduce his character's fondness for "pulling legs" and making bizarre nonsensical statements.
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 took even longer to arrive.
Tom and Pappas go to watch The Texas Chain Saw Massacre (1974) a year before it came out in cinemas.
At least two post-2000 cars are in the background when Tom and Pappas are in the cab heading to the airport in 1973.
The Citigroup Center building is visible although it was constructed
from 1974-1977.
Both Donald Trump World Tower (completed 2001) and 100 UN Plaza (completed 1986) are visible in the 1973 New York City skyline.
At the beginning of the school dance scene, a kid is screaming "Sabbath. Sabbath." Later, this kid is revealed to be the DJ, and when he's changing records, his voice still screams "Sabbath. Sabbath" in the background although he's not saying it.
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.