Other mistake: When Superman and Lois are flying through the clouds, there are a number of shots in which we see Superman from Lois' point of view. If you look closely, you can see that Christopher Reeve is not being suspended in these shots, but is, in fact, kneeling to look as though he is flying. You can tell by the profile of the red trunks.
Other mistake: In the Disciplinary/Probation Hearing scene, the State Flag behind the Council is that of Tennessee. On the Double Secret probabtion edition, narrator John Landis says "Faber College in Pennsylvania". (01:01:00 - 01:06:00)