Pipe Dreams - S3-E11
Deliberate mistake: When Zack brings an oil covered Becky to the biology teacher, you can see that it's a fake duck.
The Trouble With Mr. Bean - S1-E8
Deliberate mistake: When Bean is putting on his socks as he is driving, his foot presses the horn in the centre of the steering wheel. Except that the horn control is actually on the right-hand column stalk (you can see the horn symbol on it). This was most likely an added comical sound effect.
Genesis (2) - September 13, 1956 - S1-E2
Deliberate mistake: When Sam ejects and lands on the ground, the closeup is a flipped shot, note the "US Air Force" is backwards on Sam's helmet. (00:19:10)