Freshman Orientation and the Inventor of the Zipper - S4-E6
Plot hole: Memaw gets a call from Dr. Sturgis saying that he has moved to Waxahatchie and would she please call him back. He does not say the new phone number, and this was well before cell phones were in widespread use by the general public, so it could only be a land line. Memaw calls him back, although she could not know the number.
Suggested correction: Just watched the clip. Sturgis calls Mary, leaves a message. She calls him back; I'd guess his local number. He says "I've taken a job there", which is what you say when you're not at the place yet (otherwise you'd say here). Says he won't be there when Sheldon starts college.
Suggested correction: Memaw could have caller ID, or she could have called information.
Caller ID was first available in December 1988, and it's unlikely that Memaw would have it that early. The story takes place before that time. It is possible that she called information, but when did she do it?
A Musty Crypt and a Stick to Pee On - S4-E5
Revealing mistake: When Georgie is imagining what it's like to be a father Jana is shown holding two babies in her arms. You can tell that the babies aren't real they are just dolls.