Factual error: Kramer gives Jerry a two-line phone for his birthday, which Jerry plugs in and immediately uses. But a two-line phone requires the installation of an actual additional phone line. What Jerry was using when the NYU reporter overheard him "admitting" he was gay was simply call-waiting.
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.
Revealing mistake: After The Old Man's dentures are destroyed in the garbage disposal, he shouts that his dentist is "downtown." There is sibilance audible in his production of the T sound (after the stop release). Sibilance is high frequency noise cause by turbulent airflow directed at the front teeth vibrating randomly in a small space; if he had no front teeth, there should be no sibilance. (00:14:35)
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.