9:40 in, Patrick Stewart (Captain Picard) Flubs a line, calling Lieutenant Commander Data "The Admiral"
Brent Spiner, who is a jokester, replies deadpan and in character - "Captain, I do not believe you have the authority to promote me to the rank of admiral." He even remembers that data "cannot" use contractions. Ironically enough, that was the worst episode of TNG ever, due to a writers strike it was a "clip show."
[WARNING SPOILERS OUT THE ASS] Do not watch the second link, or read further if you have not seen BSG season 3. I don't use spoiler tags, but consider yourself warned.
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2:31 in, Aaron Douglas flubs a line spectacularly. Between season 2 and season 3 a lot of poo goes down, stuff changes, and Adama is promoted from Commander to Admiral. In the scene, Chief Tyrol is dismissive of the Admiral, but in the flub he takes it a bit too far.