Continuity mistake: Kramer's moussed up hair looks much different in the first shot compared to the rest of the scene; it's way slicker and frizzles up right after the first cut. (00:00:55)
Character mistake: George says that he's paying the chiropractor only half of his $75 bill. However at the end episode Jerry tells George that he gave the chiropractor $35. (00:12:50 - 00:19:20)
The Jacket - S2-E3
Continuity mistake: When everyone gets up from the lobby seats talking to Alton, George's coat is folded on his arm in two different ways that alternate between shots. (00:17:40)
Continuity mistake: Jerry was forced to take the phone call thanks to Kramer. He is holding the receiver in a different way between shots - look at the position of the index, on the microphone in the second shot. (00:03:50)
Continuity mistake: In the hallway scene at the beginning, Jerry is holding a magazine. When the man comes out of the elevator, he is holding the magazine The Opposite way - easy to tell because of the Marlboro ad in the back, now flipped. (00:01:55)
The Robbery - S1-E2
Character mistake: When Jerry is selling his couch to Elaine, he tells her to take it out of the door and leave - but since the arrangement is that she would move to his place, that does not make sense. (00:12:10)
The Robbery - S1-E2
Continuity mistake: Jerry is being grumpy on The Couch with his friends for giving up The Apartment, arms crossed. Notice his right sleeve, down till the wrist. When Carol enters the room with her husband for the first time, Jerry is still with his arms crossed but the sleeve is up, mid-length. (00:20:35)
The Robbery - S1-E2
Character mistake: At the end of the episode, the waitress introduces her next door neighbour, a hot redhead. After saying her line, she leaves, and George says "Nice to meet you..." and is stuck shaking hands with Carol, who he already met before and invited him to the party to begin with. (00:21:45)
The Statue - S2-E6
Continuity mistake: When Kramer gathers the old clothes, shoes, hat from the cardboard box on Jerry's table, they keep changing position in his arms between shots. (00:04:30)
Continuity mistake: When Elaine passes the newspaper to George, Jerry is sitting normally in the first shot, leaning with his right arm on the backseat in the next. (00:03:10)
Continuity mistake: George drinks from the bottle of anti-acid medicine, puts the lid back on, then at the "Yes, she wants me to like her" bit the lid is off again. (00:08:40)
Character mistake: Jerry is shopping with Vanessa; in the store there's a sign with a special offer for the salad bar, "À la cart", instead of "À la carte" (00:05:30)
Continuity mistake: Elaine tells Jerry about the ex with the unclean bathroom. At the end she puts her lollipop in her mouth twice in two separate shots. (00:07:00)
Continuity mistake: When Jerry says that Manya's widow is moving to Phoenix, Julia Louis-Dreyfus ' teacup turns 180° between shots. (00:16:15)
The Robbery - S1-E2
Continuity mistake: Jerry is back from Minneapolis, and he puts The Keys down on the kitchen isle. When Elaine walks in with the plunger, The Keys have moved forward and more towards the center. (00:04:45)
The Robbery - S1-E2
Continuity mistake: During the initial conversation when the camera is on Elaine there's a chair prominently featured in the background, with a jacket on the back. The chair turns around between shots - in particular, when Jerry proudly proclaims himself "Master Packer" it is positioned at the desk instead of facing towards the camera. (00:01:10)
The Robbery - S1-E2
Continuity mistake: George is chatting with Elaine as he is waiting for Jerry. Elaine splits an Oreo cookie. When he mentions her "price range", she is not seen fully but her left hand is in frame and she brings it up. When George turns around to address Jerry though, it's her right hand to be raised. (00:03:20)
The Stakeout - S1-E1
Continuity mistake: Jerry and his mom are playing Scrabble; when she is picking the non-existent word, Jerry says that he's "nervous." Look at The Note between his hands. At the cut, the paper is in a different position and orientation. (00:17:45)
The Stakeout - S1-E1
Continuity mistake: When Jerry is making the "Lo Mein" joke inside the video store, he is waving his hands around. The hands are out of frame; still his right hand pops in view twice showing he is holding a tape - but he is holding none before and after and he positioned himself away from the shelf. (00:01:35)
The Robbery - S1-E2
Continuity mistake: George sits down at the diners' table with Jerry after his bathroom (and mirror) break. When Jerry asks him "So what are you getting?" he is holding the menu in a different way between front view and reverse. (00:18:40)
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.