Revealing mistake: When they're dancing on the bowling alleys, they couldn't be waving their bowling balls about as if they were made from foam - bowling balls are heavy!
Suggested correction: Bowling balls can weigh as little as 3 pounds.
Continuity mistake: Dimucci is wearing grey trousers when they start singing Prowlin, but he has jeans on for the second half of the song.
Suggested correction: That's because it's gone from the night out with the gang to the next day at school.
I'm not sure about this "correction." Every other song in this film is done in real time, why would this particular song take place over 2 days? Since the rest of the T-Birds are in the same clothes, and Dimucci is wearing the same shirt, I would say it was a mistake that his pants changed.
They are all wearing different clothes except possibly Johnny. Goose goes from a flannel shirt to a blue T-shirt. Davey goes from a brown shirt to a yellow shirt. DiMucci goes from a red shirt to a blue/grey shirt. Johnny is wearing all black, but he does so in every scene except at the bowling alley. The start of the song is at night and the second part is at school, meaning they would have to be there during the school-day or just after when they would have access to the auditorium.
Other mistake: During the bike chase at the bowling alley, when the line "don't know who you are" is sung, a guy on a car hood throws his body to the right as if he were pushed by an invisible hand but in the next shot he repeats the motion when a bike hits the car he's sitting on.
Suggested correction: I've watched this scene several times since this I saw this post and can confidently say that the guy was going along (dancing?) with the music on the first instance of his motion; he is in perfect timing with the line you referenced.