The Wedsworth-Townsend Act - S1-E1
Other mistake: At the start, on the way to the structure fire one of 10's rigs has license plate number E180174, but at the fire we see 127's engine has the same license plate number E180174.
Other mistake: When Frank's with Margaret in her tent and she tells him that she thinks they should reevaluate their friendship, there's a Life Magazine lying on her bed which is dated over 15 years in the future - August 25, 1967, with "The other war in Vietnam" written on its cover.
Other mistake: In the opening credits, Bob answers the phone. None of the buttons light up when the phone rings. On that style of phone, the light would indicate which line to answer. The phone is obviously a prop.
The Thanksgiving Story - S2-E10
Other mistake: During John-Boy's entrance exam at Boatwright University, when he's given the pamphlet and history test questions, note three of the questions include the contraction "it's" which is incorrect within those given questions. Each question should have used "its" without an apostrophe. Additionally, the sign on the University's wall reads "keep your eyes on you own paper" instead of "your own paper." (01:00:35)
Other mistake: The gender of Mrs Slocombe's cat is always different in each episode. Sometimes her cat is a female and other times it is a male. (eg. In 'Mrs Slocombe Expects', her cat is female. In 'No Sale', when Mrs. Slocombe complains about her having to get up to have a bath at 6:00 in the morning, she says, "The gurgling of the tank woke him up.").
Blödeln auf die feine englische Art - S1-E2
Other mistake: In the "Happy Valley" segment, when the witch is just about to enter the cathedral, you can see a car drive past through the windows behind the altar. (Now, this is Monty Python, so we have to be careful... But is isn't clear, or funny, enough to be there on purpose).
Other mistake: Near the end, after Fred says, "If you take my hearing, you might as well take all of me, " Lamont turns off the lights by flipping the light switch up. A moment later, Lamont turns the lights back on by also flipping the light switch up.