Factual error: On the castle where King Henry VIII is supposed to live, the flags at the top have the pattern of the English flag, being a + shaped cross on a coloured background, but it should be a red cross on a white background. Instead it's a white cross on a blue background. Those are the colours of the Scottish flag, but England and Scotland were separate countries at that point in history. And the cross on the Scottish flag is an X shape rather than a + shape anyway.
Continuity mistake: Right at the beginning of the episode when all the children are on the bus we can see that in front of Nelson is Bart and behind him are Lewis, Martin and Wendall. Then when the shot changes to behind Nelson, Lewis has swapped places with Bart, Bart has disappeared and some weird kid is sitting where Lewis was. (00:00:40)
Continuity mistake: Right at the end Lisa is holding a doll head and some cards. There is a very brief shot of Bart, and then when it's back on Lisa she doesn't have anything in her hands when they hug. There wasn't time for them to be put down and you cannot see them anywhere either.
Continuity mistake: Milhouse is holding the Monopoly set in the Simpsons house. Then when his Dad comes in he isn't. Granted he could have put it down, but it isn't anywhere we can see, so he would have had to put it down behind the sofa which is somewhat unlikely.
Factual error: The tongue Lisa sleeps on in the museum isn't anatomically correct. It shows the bitter and sweet taste buds as being side by side on the surface of the tongue. In reality, different taste buds are not in specific places on the tongue. I wouldn't normally complain, but this is supposed to be in a museum.
Continuity mistake: When the Simpsons first see Artie Ziff in the attic, as he stands up, there's a theremin behind him (corresponding with Homer's comment that the "ghost" was playing his theremin). Artie puts a sign up above it. However, when Artie moves to the rafters, the sign he put up is still there, but the theremin isn't.
Continuity mistake: At the Randall Curtis's Ranch we see Randall Curtis ride off on a Ton-Ton to go to the video store but in a scene only a few minutes later we see Marge and Homer drunk, tossing him around. Unless the video store is on the ranch or very close by this doesn't seem possible for someone so determined to rent movies.