Revealing mistake: While Jack is leaving The Apartment after giving Jerry The Pen, you can see they have put a fake background outside the front door. What's more it is not even that realistic. It looks like a forest with a river in the middle. The Seinfeld's Florida apartment is situated amongst many other apartments around it.
The Nose Job - S3-E9
Revealing mistake: When George is talking to his girlfriend about the possibility of getting a nose job, Elaine is visible in the other room waiting to make her entrance.
The Suicide - S3-E15
Revealing mistake: In this episode when Jerry leaves his room to talk to his neighbour about their fight, when he shuts his door the wall shakes revealing that the place he lives in is not a real apartment.
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.