Factual error: In the episode where Jerry is upgraded to first class while Elaine struggles in coach, the scene changes to show a plane flying with the colors of Southwest Airlines, and you can make out the name "Southwest" written on the tail if you pause as it's landing. Anyone who has flown them knows that there is no first class on Southwest.
Deliberate mistake: In this episode Elaine angers the bag man and he puts her bag on a plane to Honolulu. When Jerry and Elaine arrive in New York and are waiting for their bags, it cuts to the "Hawaii" airport and shows Elaine's bag coming out to the baggage claim belt. This was a deliberate mistake as there is no way Elaine's bag could have gotten to Hawaii at the same time Jerry and Elaine are waiting for their bags in New York, since they only left from Missouri.