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)
Continuity mistake: Jerry says that he wants to suggest to his current girlfriend, Vanessa, to go away for a couple days. George starts saying "No no no" and before the cut he raises his arm and lowers his head as to express concern. But in the new shot there's no trace of that change in posture. (00:02:45)
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: Jerry orders a tuna sandwich, and Elaine turns towards him and whines "Tuna?" Her hand is still on the menu, but when the angle changes her hand is on the neckline of her top. (00:04:50)
Continuity mistake: The scene with Elaine on The Couch plotting the demise of the cats begins with a nasal spray on the kitchen counter. There's no trace of it after that initial shot, and it reappears only when Elaine comes closer for her cup of coffee. (00:13:00)
Continuity mistake: Kramer runs off to meet the girl he just spotted through the binoculars, and George walks through the door and crashes on The Couch. The pillow is straight-ish, very angled and straight again during the conversation, with George's hand changing position between shots. (00:15:45)
Continuity mistake: Elaine comes out of the bathroom sniffling and with a big stripe of toilet paper. She rubs her left side of the nose when she asks "Didn't work, huh?" In the next shot with George answering with a burst of nervous laughter, Elaine's hand is in a different position, and George himself is clutching a tissue to his chest. (00:16:25)
Continuity mistake: Up in Vermont, Jerry is beginning to have a rather tense conversation with Vanessa. In the close-up after the watch comment (when he is thinking of the delightful drive home ahead) Seinfeld is all smiles, but in the shot before and after he is staring with a tense expression. (00:17:20)
Continuity mistake: When Elaine joins Jerry and George at The Cafe and tells them she spent ten minutes looking for a grape, keep an eye on the straw in George's drink. From shot to shot, the straw in George's drink keeps changing position, from tilted to upright, then tilted at The Opposite end of the glass, then upright again, then back to tilted.
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.