The Hot Tub - S7-E5
Deliberate mistake: When Elaine comes home and doesn't find Sean Paul there, she runs to her neighbour across The Apartment. The neighbour opens the door and stands outside it then the door slowly closes behind him. Suddenly, the door opens again with a swoosh without anyone being there. Because the camera switches angle right after this, it is apparent it was opened to gain this shot or to at least permit it continuity wise. (00:16:40 - 00:17:10)
Deliberate mistake: When George is watching Home Alone, the sound effects and music that are heard aren't actually in the film.
Deliberate mistake: Jerry's apartment is on the fifth floor of his building, yet any time he buzzes somebody in from outside the building, they enter his apartment in a matter of seconds.
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.