The Trouble With Trillions - S9-E20
Deliberate mistake: When Homer is being interrogated by the IRS, his package is briefly replaced by a ball of string when the IRS agent sits down in the chair and spins around.
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.
Deliberate mistake: Richie was an infant in season one, and beginning with this season, he has been aged up to at least 3 years old while none of the other characters have aged up.
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.