The Suicide - S3-E15
Other mistake: While George is talking to Elaine and Jerry in Jerry's apartment, Jerry and George talk about how George's mother and father are both bald. We know from later episodes after his parents are introduced that they both have hair.
Answer: Composer Jonathan Wolff used a synthesizer, although in seasons 7-9, a real bass is used in addition. Wolff also recorded himself making hundreds of mouth noises, pops, and slaps to add to the synthesized bass licks so that each episode has a different theme. The only real "back-story" is Jerry Seinfeld was having trouble coming up with a theme song and talked to a friend who happened to know Wolff. They wanted to avoid that cheesy late 80's sit-com theme song and Wolff came up with what we enjoy now. Jonathan Wolff has also talked about this further in interviews, recently Reed Dunela interviewed him, so for a fuller account of his story; check out "The Wolff of 116th street".