Me and Mr. T - S1-E4
Continuity mistake: When the teacher is asking the class questions about the declaration of independence, she has some info about it written on the blackboard ending with "1776 in." Then facing away from the blackboard, she asks a question and Mr. T quickly answers and then only a second later, the camera is back on the teacher and suddenly the world "PHILADELPHIA" is on the blackboard under the "1776 in" with no time for her to have written that word in one second.
Factual error: There is an intercom system in the library that is used by Derek (and at the end, Edward). They try pushing down the buttons to talk (which is normal for intercoms), but then each time, we are hearing Ricky and his grandfather's conversation from inside the car that's outside without using the intercom connected to the house. In the 80s, a house intercom system would not pick up a conversation in a parked car outside.