Factual error: At the end of the episode in which George and Susan get engaged, they are lying in bed together watching "Mad About You" on TV. However, at some earlier point on "Mad About You" it had been established in a crossover episode that Paul Reiser was the person who lived in Jerry's apartment before him and was an old acquaintence of Kramer's, meaning that "Seinfeld" and "Mad About You" existed in the same reality. On "Seinfeld," the show "Mad About You" could not exist.
The Sponge - S7-E9
Factual error: During the AIDS walk there is an officer seen several times with a patch "Transit Police, NYC." Not only is the patch completely fictional, it doesn't look anything like the real transit police logo. The Transit Police had already been defunct by the time of this episode.
The Calzone - S7-E20
Factual error: When Jerry gets a speeding ticket, he asks Nicki to give the officer the registration. She gets a large piece of white paper from the glove compartment. That's what car registrations look like in California, where the show was produced. In New York, where it's supposed to take place, car registrations are the size of a driver's license, and are usually kept in the driver's wallet.
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.