Other mistake: When Mr. Bavalaqua is telling Jerry and Duncan the rules for the big race, there is a male extra right behind him who is mouthing Bavalaqua's lines as he's talking. (00:21:00 - 00:22:00)
Other mistake: When George and Elaine are arguing about a bald woman rejecting him because he's bald, he says, "No one walks into a beauty parlour and says, 'Give me the Larry Fine.'" Larry Fine, who was partially bald like George, was a member of the Three Stooges. George should have said, "Give me the Curly Howard." He was another member of the troupe, and fully bald.
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.