Continuity mistake: When the cable guy tells Jerry it'll cost him 400 bucks, he is holding the plate with the cake in his right hand, but in the following shot the left hand is holding just the fork. (00:19:10)
Continuity mistake: George walks confidently to his ex and calls her by name. Leslie's friend is taking a bite from a little celery stick, but in the following shot her hand is lowered in front of her chest. (00:16:45)
Continuity mistake: In the opening shot of The Baby Shower party, Leslie turns towards her friend and starts talking as a ponytailed woman walks in the background. The same happens in the close-up that follows. (00:12:35)
Continuity mistake: Kramer keeps pestering Jerry with the offer of the illegal cable. On the table behind Jerry, the position of the remote and the cable keep changing between shot in the first part of the scene. (00:06:00)
Continuity mistake: George sits in Elaine's spot and puts his wallet close to a glass of water and a used tissue. When he gets up in the next shot, the glass is further back on the table, past the small plate and closer to Elaine and Jerry. (00:05:40)
Continuity mistake: Elaine sits by Jerry to ask him permission to hold The Baby Shower at his place. Jerry is holding a morsel of food in his hand, gone at the first cut. (00:04:20)
Continuity mistake: Reminiscing about the incident with the performance artist, George says that she was aiming at him with the chocolate syrup "like she was putting out a fire." Notice Jerry has nothing in hand. Next shot and he's clenching a paper tissue. (00:02:40)
Continuity mistake: Kramer tries to stop Jerry from running towards the door. "Agent Stone" in the following shot has his badge in the left hand (was in the right earlier) and reaches with the right for his gun under The Jacket. But there's another shot, with cornflakes and other things being blown up by bullets, when Stone is still showing his ID in the right hand. (00:09:00)
Continuity mistake: In the shot when she protests that the husband with the chipper name is only a Kennedy by marriage, Elaine is holding a paper towel, not quite in continuity with what comes before and after. (00:01:35)
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.