Deliberate mistake: The car Rudy, the mechanic, is working on is a 1971-72 Plymouth (the one where the chassis falls down around him). Plymouth's of that era were unibodies, which means that the body and the chassis were all one piece and not separate, so there's no way a chassis could have fallen down like that from that particular car, since it didn't have a separate chassis.
Deliberate mistake: When the geek and the prom queen are driving along in the Rolls-Royce rebel yell scene, the close-up shot of them through the windshield shows a missing rear-view mirror. It was there when the geek pulled out of Jake's garage and it reappears later when the Rolls is parked in front of the house where John Cusack's character lives. This was probably a deliberate mistake by John Hughes so that he could get a better shot of the prom queen feeding birth control pills to Anthony Michael Hall.
Deliberate mistake: As David runs from the MPs in the restaurant, he jumps off the balcony onto the bar below. It is very obvious that it's the stunt double for Michael Pare doing the jump. (00:45:35)
Deliberate mistake: Before going on stage in the infamous purple coat for the first time in the movie, the Kid is in his dressing room. The silver jewelry/decoration on his coat is on the left shoulder. In all subsequent shots, the silver jewelry/decoration is on his right shoulder.
Deliberate mistake: The soles of the boots Daisy the cow is wearing have been removed to allow her to walk properly. In some shots, their lack of soles is evident.