Other mistake: When Eric is ordered to go to his room he mentions that Feeny used to be his 6th grade teacher. However, later in the series it is emphasized several times that Mr. Feeny was Cory's teacher every grade he was ever in. With Cory only being 3 years younger than Eric, it would not be possible for Feeny to have been Eric's 6th grade teacher as Cory would have been in 3rd grade and had Feeny as a teacher per what is stressed on multiple occasions later in the series.
Continuity mistake: When Mr. Feeny says "As if you are returning for your 20th high school reunion", there is a red crown on Mr. Feeny's desk with Minkus sitting on a chair at the end. After the camera cuts to a close up of Minkus saying 'More like a pre-union", there is a cut to Mr Feeny who turns to him. Minkus is all of a sudden holding the crown on his lap, then he is seen putting the crown back onto the desk. (00:04:00)
Continuity mistake: When Alan is talking to Cory in his room, telling him that he can always come home, he is pointing his finger at him. He has his right arm rested on his legs and is pointing with the left arm. Just before the shot changes to face Cory, Alan stops pointing. In the next shot, facing Cory, Alan has his left arm resting, and is pointing with his right arm.
Plot hole: After Shawn leaves Cory's house to get a pizza, he calls Cory on the phone literally a minute later to tell him that Lenny Dykstra is at the pizza place. There's no way Shawn could have left Cory's house, walked to the pizza place, spotted Dykstra and either asked to use the restaurant's phone or found a pay phone to call Cory in such a short amount of time. (00:13:30 - 00:14:45)