Deliberate mistake: Although it was done for plot purposes, no school photographer would only take just one shot of a class photo. They generally take up to 15 to 20, as it is difficult to get everyone to look at the camera and smile at once (and hopefully not pull silly faces).
Deliberate mistake: When the family is trying to get money from Al at the start of the episode, he throws it on the ground making the rest of the family to dive on it and you can see Bud get it, then throw the bunch of money in the middle of Kelly, Peg and Bud so they can all get to it instead of taking it all. (00:02:10)
The High Life / Best Friends - S2-E10
Deliberate mistake: In "The High Life", there is a scene where Stinky submerges his head in a tank of water. He delivers the line, "Gee willickers, it's still ticking", and everyone somehow understands what he is saying with his head underwater.
Suggested correction: Nobody responds to what Stinky says, so there's no reason to assume that everyone understood him.
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.
Deliberate mistake: Morgan turns on the stereo and starts dancing on the sofa with her doll. She then tosses her doll, which tips over a plant and breaks the glass on a set of French doors. The stereo magically stops the moment the glass breaks.