Corrected entry: When the magician pulls the scarf from Mr Bean's jacket, you can see that the scarf is already in Mr Bean's jacket and the magician just takes it out. But since Mr Bean showed up late to the magic act, the magician would not have had any chance to put the scarf there before Mr Bean came up to the stage.
Corrected entry: When Mr Bean arrives with his new TV, the room is dark, so he has to switch on the light. However, when he starts undressing, he closes the curtains, which were open, and it's daylight outside: so the room should have been light when he arrived.
Correction: If you take a look inside his home, its a very dingy studio flat with dark colours, explaining why it is so dark when he comes home.
Corrected entry: The TV shouldn't work at all as Bean didn't wire the plug up - he simply pushed the cable into it.
Correction: Obviously. Its an intentional gag. This doesn't even class as a mistake.
Correction: The way the magic trick works (in the show and in real life) is that the magician, using slight-of-hand, places the scarf in Mr. Bean's jacket without anyone seeing (reverse pick-pocketing) as he's getting on stage, not before.
Bishop73