Audio problem: In the scene where Penny and Johnny are teaching Baby their dance routine you see Penny putting on a record, if you look closely you can see that Penny moves the arm to put the record on then right away you see her taking the arm away even though the music has started. Even if it's a directorial device for us to hear different music than they do, it's still a mistake because she's not actually put the record on, meaning they've not got any music playing.
Continuity mistake: When Max is talking with Tito at the end during the final show they're both talking and standing next to the record player. In the next scene they're both standing way off stage (no longer next to the record player) and then Max enters on stage and Tito walks up behind him.
Continuity mistake: In the scenes where Johnny and Baby have to break into the car, when Johnny looks in to find his keys, it's raining, when he turns to grab the post to break the window, the sun is up and the ground is dry, then when he turns back to actually break the window, it's raining again.
Continuity mistake: During the entire part where Penny is sick after the abortion, Baby's hair alternates between really curly and wavy. When she gets out of Johnny's car it's wavy, when she runs down to get her father all the way up until the part where her father sees Penny it's curly, after that it becomes wavy again.