Other mistake: When the kids are opening their lockers, they enter the code, then pull on the lock to open the locker. The closed lock is still attached to the front of the locker. When they close it, it's magically locked again without them ever opening or closing the lock. In reality, these locks would be useless, or the locker doors wouldn't open.
Other mistake: In the scene where Yakko, Wakko and Dot are sitting at their desks repeating Miss Flamiel's every word, Wakko is drawn without legs (only feet) during one shot.
Other mistake: When King Richard asks the chef if there's lemon in his tea, he replies "Yes, my king. Some 'and-squeezed lemons." The closed-captioning says "Some unsqueezed lemons." (00:15:40)
Other mistake: During "My Freeze Ray", there's a shot where Billy, Penny, and several other people open doors to the laundry machines in sequence. When Billy opens the door to his machine, you can see the reflection of everyone else just standing there, waiting for their cue to walk forward.