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.
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.
In the butcher shop, about 12 minutes into the movie, 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.
Reverend Duncan says that the school's Bible class is being renamed "Ethics" due to requirements of church/state separation, even though 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.
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.
When Tommy is hiding under the hospital bed after euthanizing his mother, his feet are sticking out the side of the bed. The people working on his mother (who for film purposes have to be unaware of his presence) have to move around his feet they are sticking out so far.