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.