The goof about him saying he was 5 or 6 when in a play about the Holocaust is probably wrong (but to by much), he was probably 7 or 8 and it could have been about Kristallnacht, also referred to as the Night of Broken Glass. A major Antisemitic event in 1938 Germany. Shatner was 7 when that took place. Also, there was numerous Antisemitic violence before that time in Germany.
Right after the scene showing Captain Sisko 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.
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.
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.