Homer Badman - S6-E9
Character mistake: When Grandpa is putting up the American flag for Homer's public access show and Marge says the flag only has 49 stars, there are actually only 38: 8+7+8+7+8.
Character mistake: When Hugh proposes to Lisa using the electronic signage, he spells the word "honor" using the American English spelling. Hugh should have used "honour" as this part of the show was set in England, and Hugh is from England.
Character mistake: Burkina Faso is listed as being among the Southern Hemisphere locations Bart called when Homer is looking over the phone bill; since Burkina Faso is completely within the Northern Hemisphere, it would have made no sense for Bart to call there.
Suggested correction: It may not make sense, but Bart isn't exactly the sharpest tool in the shed. In this same episode, he looked at his globe and thought Rand McNally was a country and was convinced by Lisa that the citizens there wear hats on their feet and that hamburgers eat people. Additionally, he could have just decided to prank call someone there if for no other reason than he thought the name of the country was funny.
Entirely possible, but since Bart had a globe right there to refer to, even someone with his limited geographical knowledge would have been able to tell that Burkina Faso is in the Northern hemisphere, unlike the other locations he did call as depicted in the montage (Antarctica, Argentina, unspecified South American nation, etc).
Another Simpson Clip Show - S6-E3
Character mistake: In the first scene, Marge says that it is 9:30pm, but after Homer's flashback, the clock next to Homer reads 11:50.