Plot hole: When Elaine meets Glenn's welfare case worker at The Apartment, the case worker does not tell Elaine that Glenn actually has a wife (after clarifying that she isn't The Wife). This is pure plot convenience. When Glenn's wife finds Elaine in The Apartment, he says "You're home early." She lives there, they are not separated, and surely the case worker would be involved with both of them, not just Glenn.
Continuity mistake: When Loretta comes into The Apartment she is carrying a coat and roses in one hand and the other hand is supporting her handbag by her right shoulder (left on screen). In the next shot she is holding the bottom of the flowers with both hands instead of just the left hand.
Continuity mistake: When Kramer and Jerry are talking about the bird being in the hallway, notice how the intercom keeps changing. In some shots the intercom is not set straight and leaning to the right and in other shots it is completely straight. The most notable change is when Kramer is leaving The Apartment. It goes from crooked as he is leaving, then straight while he is outside in the hall and then the entire unit is completely pulled right out after Kramer rushes backs in.
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.