The Outing - S4-E17
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.
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.