Character mistake: When George and Elaine go to the coffee shop after The Movie without Jerry, they establish that Elaine moved to NYC in 1986. Then they make fun of the way that Jerry throws up; both imitating Jerry. The "Dinner Party" episode is after the "The Dog". In the "Dinner Party" episode, Jerry brags that he hasn't thrown up since June 29th, 1980. The black and white cookie ended this streak. Elaine would not have been around to see this, not arriving in NYC until 1986.
The Library - S3-E5
Character mistake: When Marion mentions Mr Bookman she says he'd been on the job for 25 years. Yet later on he tells Jerry he's been on the job since 1971, which in 1991 makes it 20 years.
The Letter - S3-E21
Character mistake: When Lippman is recounting his conversation with his accountant, he mentions that the accountant, a man, gave the tickets to "her daughter."
The Fix-Up - S3-E16
Character mistake: George calls Jerry to tell him about sex with Cynthia. He starts by saying he just got home, which Jerry repeats. A few lines later, George confirms they had sex at his own apartment. Why would he be getting home from his own apartment? (00:13:50)
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.