Hair By Mr. Bean of London - S1-E19
Continuity mistake: In the scene at the country fair, Mr Bean interrupts a boy doing the buzzer game. When Mr Bean is on his second go at this puzzle and stands up after unplugging the device, you can see the same boy come round a table behind Mr Bean. Cut to the next shot, the boy has disappeared from where he should be behind Mr Bean and can now be seen walking across the back of the hall.
Love 'Em and Leave 'Em - S1-E8
Continuity mistake: After Luigi says "Let's play cupid," he peeks around the corner along with Peach and Toad down at Mario going down the aisle with his "bride-to-be." Luigi, as expected, has been wearing green all episode, but when you see them peeking around the corner, Luigi's hat has become red. In the very next shot showing Luigi from behind, his hat has returned to green. (00:14:40)
Jimmy - October 14, 1964 - S2-E8
Factual error: The episode is set in 1964. When Frank and Jimmy first arrive at the dock and some of the dock workers are harassing Jimmy, there is a nice set of period appropriate cars in the foreground that the other dock workers are around, but in the background we see street traffic with 1980s cars driving by. (00:10:50)