Audio problem: After Spicoli crashes Jefferson's car, Jefferson's brother says "My brother's gonna kill us - he's gonna kill us" yet his mouth isn't moving during those lines (even though shown from the back you can still tell). Then camera faces him and he now matches the words.
Continuity mistake: When Rat approaches Stacy at the check-out to ask for her phone number, the characters in the background keep changing. Sometimes you see Damone standing there; other times there are different people.
Plot hole: In the very beginning at the mall, where the older guy comes in to the pizza shop and sits in Stacy's section - the co-worker says "she's not even in high school yet." First of all, the school she's at is "Ridgemont High", and secondly, if she wasn't in high school (which would mean she would be younger than 15 at least) - how could she have a job, where the minimum age is at least 15? Even by mall standards, it's doubtful they would hire someone who is 14.