Continuity mistake: In the pilot episode "Good News, Bad News", look out when the waitress discusses the two coffee pots. She says "Trusts me George, nobody wants to see you on caffeine", and the unbuttoned top of Jerry's jumper is noticeably folded - but straightens instantly in his reaction shot. Also it should be noted that she walks away without actually pouring coffee to George - you have to assume a little amount of time elapsed between that reaction shot with Jerry and the following on George. (00:01:45)
Continuity mistake: Jerry's apartment in the first episode was on the fourth floor. Then in the next bunch of episodes it was 3A. It then changes to 5A for the remainder of the series.
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 Stakeout - S1-E1
Continuity mistake: Throughout the video store scene, a golden sticker keeps switching position on the adult tape Elaine is holding; The Switch can be noticed particularly easily when they talk about the wedding; Elaine repeats "A wedding?" and the box has no sticker, but few seconds later she laughs about the combover and the sticker is showing. (00:02:50)
The Stakeout - S1-E1
Continuity mistake: Jerry is playing with his mom; she handles him a note with Elaine's message. He says "I am such a jackass." His mom asks "She knows... what?" In that shot, Liz Sheridan 's hand is nowhere near her face, where it should be to match the shots before and after. (00:16:55)
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: In the video store, we see Elaine put back Cocoon 2 and then doesn't pick up another video. But when she takes the video from Jerry, she's holding a video in her other hand.
The Stakeout - S1-E1
Continuity mistake: At the video store, when Jerry shows Elaine the adult video, he holds it with both hands with his right hand fingers under the box. In the next shot, he's holding it with only one hand, with his right hand holding it by the side.
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: When Jerry tells Elaine to "Do it in the shower", he gestures with his fancy retractable umbrella. But he is holding it by opposite ends in the two consecutive shots. (00:02:30)
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 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: Jerry has just won the contested deed for The Apartment beating George. Look at The Jacket on the counter. When Kramer makes his trademark entrance, The Jacket is placed differently. (00:16:40)
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)
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)
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)
Continuity mistake: In Jerry's apartment at the beginning, Kramer hands Jerry the telephone. Jerry takes it with his right hand, but in the wide angle he is holding it in the left hand. (00:03:40)
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: Elaine joins the other late at the table. She sighs and puts her sunglasses on the table, above an open menu. Brief cut to George, and the menu is on top of The Glasses. It is again at the bottom later. (00:01:45)
Continuity mistake: During the initial conversation, George keeps playing with the paper sleeve of a straw in certain shots, while his hand is in another position in the reverse shots (noticeable for instance when he says "Guys with cats...I don't know..." (00:02:30)
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.