Continuity mistake: When Jerry's sitting with George in the hospital talking about George's jacket, as Jerry says "no, I tried it on, it fits good", he's gesturing with his left hand, which he then puts in his lap. From the reverse angle though, his left hand's still raised, then he lowers it again.
Character mistake: When George and Elaine go to the coffee shop after the movie without Jerry, they establish that Elaine moved to NYC in 1986. Then they make fun of the way that Jerry throws up; both imitating Jerry. The "Dinner Party" episode is after the "The Dog". In the "Dinner Party" episode, Jerry brags that he hasn't thrown up since June 29th, 1980. The black and white cookie ended this streak. Elaine would not have been around to see this, not arriving in NYC until 1986.
Continuity mistake: This mistake is in the Calzone episode. Towards the end when George walks in and his boss is looking around for the smell of calzones, George is holding a bag in his hand. In the next shot that shows the back of the boss's head the bag is now on top of a box that George is carrying. When it goes back to a close up the bag is in his hand again.
Continuity mistake: In the episode "The Suicide", Kramer discusses suicide with Jerry, and says that he'd give someone 72 hours to come out of a coma before all his property is up for grabs. However, in the episode "The Comeback", Kramer tells Jerry that he never knew that people could come out of a coma.
Other mistake: The tenant board member tells George that Mr. Eldrige in apartment 8C has decided he wants the new apartment. However, the new apartment in question has a 3-digit number - 808 I believe. This indicates that the building would not have single digit numbers and letters (Such as 5E, 8C, etc.) as part of its numbering system.