The Ticket - S4-E4
Continuity mistake: George is in Jerry's apartment and he is unshaved, maybe a 2-day beard. However in the next scene after he leaves The Apartment with Jerry, he is shaved again.
The Airport - S4-E12
Deliberate mistake: In this episode Elaine angers the bag man and he puts her bag on a plane to Honolulu. When Jerry and Elaine arrive in New York and are waiting for their bags, it cuts to the "Hawaii" airport and shows Elaine's bag coming out to the baggage claim belt. This was a deliberate mistake as there is no way Elaine's bag could have gotten to Hawaii at the same time Jerry and Elaine are waiting for their bags in New York, since they only left from Missouri.
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.