Revealing mistake: When Jerry is slamming the payphone in frustration with Elaine, he slams it on The Switch-hook multiple times. Pressing down The Switch-hook like that would end the call. Clearly Jerry is not really connected to Elaine on the phone. (00:14:05)
Continuity mistake: When George is at the window making a complaint, a cut reveals several inconsistencies. The man at the window has his arms in a higher position in the second shot (plus his facial expression is changed), the woman no longer has her hand up on the wall, and George's left hand is suddenly resting on the table. (00:15:55)
Factual error: George asks for a nickel from Jerry for his candy bar. He then proceeds to put only 3 coins into the machine for a $0.50 candy bar. No 2 coins would require a nickel to make 50 cents.
Chosen answer: George does mention his brother in the episode "The Parking Space". They actually really never mention anything that contradicts the fact he had a brother though, it just isn't mentioned.