The Statue - S2-E6
Continuity mistake: During the scene at Monk's, Jerry bumps George on purpose making him spill some coffee. George is holding his cup in the right hand and the menu with the left. In the reverse shot you can see Jason Alexander put the cup down, held in his left hand. (00:14:20)
The Jacket - S2-E3
Continuity mistake: When Elaine's dad says "Pipe down, chorus boy" to George, suddenly a hotel staffer in red appears in the recess by the lamp. In another blatant continuity mistake, in the shot that follows George is suddenly without glasses. (00:17:50)
The Jacket - S2-E3
Continuity mistake: Elaine's intimidating father gets up and tells Jerry and George in his gravely voice "I'm going to the bathroom." The newspaper on the table changes spot before and after said shot. (00:15:30)
The Jacket - S2-E3
Continuity mistake: At the end of their strategic break in the men's room, George tosses his paper towel in the bin to the right; however the previous shot ended with Jason Alexander turning around having the towel in his left hand and glancing towards the basket on the left. (00:13:55)
The Jacket - S2-E3
Continuity mistake: In the reaction shot with Alton Benes scoffing at George and Jerry's sissy choice of drinks, a woman with a coat in hand is walking behind him, towards the door. In the next shot, no trace of the woman, just someone in a bicolor puffer. (00:10:25)
Continuity mistake: Jerry and Kramer are arguing about the bet when Kramer is having a glass of milk. The phone rings cutting them off, and Kramer's glass suddenly from his mouth goes to his hip. (00:10:25)
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: 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: When Elaine gets kicked out of the nail salon it is a clear day (in fact the whole episode is) then the next scene she meets J Peterman at night and in the rain. When she left the salon she is wearing a red blouse, no jacket. When she meets Peterman she is in a trench coat with a white blouse. The Peterman portion of this episode really makes no sense.
The Implant - S4-E19
Continuity mistake: During the wake for Betsy's aunt, George puts snacks on his plate while talking to the reverend. He puts at least 6 pieces on his plate while the next shot of his plate shows only 2. (00:14:15)
Continuity mistake: When Kramer enters Jerry's apartment, he closes the door. In the next shot, the door is wide open. A few shots later, George opens the door, which was closed when he entered.
The Ticket - S4-E4
Continuity mistake: George is in Jerry's apartment and he is unshaved, maybe a 2-day beard. However in the next scene after he leaves The Apartment with Jerry, he is shaved again.
Continuity mistake: When George enters The Cafe near the start, he takes Jerry's plate and begins eating the fries. After finishing the first fry, his hands are on the plate. Jerry then asks him what happened, and suddenly he has a fry in his hands which are also now raised slightly.
The Apology - S9-E9
Continuity mistake: When Jerry and his naked girlfriend are playing scrabble just after Jerry accuses her of stealing and it flips to the front at the bottom of the screen you can see a bra or towel covering her breasts but is gone when she stands up. (00:03:40)
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.