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 truck is slamming numerous parked cars on a residential street, it sideswipes a parked Dodge Aspen (white with tan landau top). At the lower-right corner of this shot, a white Chevy Nova is parked at the corner (its vinyl top and trim has been poorly painted the same white as the body). Both these cars are repositioned to be at the roadblock location at the end of the chase, with the Nova slammed from behind by the truck and the Aspen parked near the cop cars. (00:07:00 - 00:07:40)
Deliberate mistake: During the scene with the malfunctioning juice maker, when it goes nuts there is no possible way that all that juice and pulp could have come from just one orange. (00:22:45)
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: 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.
Deliberate mistake: When Supergirl flies out of the lake upon her arrival to Earth she's wet. When she lands on the shore she's suddenly dry.
Suggested correction: Incorrect. She's not wet when she comes out of the water. She emerges from the water dry in an (incredibly wonky) effects shot. Why she's dry coming out of the water is unclear, but it presumably has something to do with the teleportation process for how she got to Earth considering her costume also suddenly appears on her as well.
Deliberate mistake: When Betty walks away from the kissing booth it is clear that she has spike-like heels on her boots. When she steps on to the "moon" surface the spike heels are gone. Her spikes are on up to the point where they enter the room. I am pretty sure the crew did not want to puncture the bladder and have water all over the set. (01:07:25 - 01:09:35)