Continuity mistake: Jerry and George are at the pharmacy. As George pays the bill and is heading out, behind Jerry there's an old lady at the counter. The camera changes and the same lady disappears and you can see her in other side of the store heading again to the counter. (00:02:25)
Other mistake: When Jerry, George and Elaine go out to Long Island to the party, George sees his lady co worker friend who says "guess what property I just sold...129 West 81st". That is Jerry's own address, which wasn't sold to anyone.
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.