Right after the scene showing Captain Sisco on the bridge of the original Enterprise, there's a shot of Voyager dropping out of warp speed. The shot must be running backwards as no ship has even been shown to warp aft end forward.
Nana Visitor's introduction card lists her as having played Commander Kira Nerys on Deep Space Nine while in fact, she rank was a Colonel at the conclusion of the series.
In a scene with Patrick Stewart, Shatner claims to have performed in a player at '5 or 6 years of age' regarding the holocaust. However, at this age the holocaust would be years away.