Continuity mistake: George is talking about the phone call; when he says "I don't like to go too long before I ask them out", the waitress with the blue cardigan is passing behind him. At the cut, she's already to the other side of the counter. (00:02:05)
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: 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)
Continuity mistake: When George shoos away everyone from The Apartment to make the phone call, in the background you can see the pink bottle with its black lid. When he actually approaches the phone, the bottle is uncapped. (00:09:35)
Continuity mistake: Jerry says he has never seen an episode of I Love Lucy in his life, then pops the cork on the wine bottle. Then it cuts to the lady and she asks, "Is there anything else about you I should know?" and the wine bottle is still on the table, corked. Then it cuts back to Jerry, and the bottle is still in his hand uncorked. (00:11:40)
Continuity mistake: During the scene with Donna and the wine bottle, besides continuity errors with cork and glasses position already mentioned in this page, the level of wine itself changes; Jerry poured wine to Donna, but her glass is empty in some shots, and before Kramer's arrival both are full, only to become empty in the last shot. (00:12:30 - 00:14:00)
Continuity mistake: Donna's purse strap changes position on The Couch throughout the scene, when she's there when George brings up her liking the commercial.
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.