During the boxing session between Chief and the Admiral, when Chief enters the boxing ring, he has his dog tags on and does not take them off, but they mysteriously disappear in the next shots.
(In the extended cut, after the chief is knocked down after the bell rings, he picks up his dog tags and throws them out of the ring.)
At the end of the match between Hotdog and Starbuck, she knocks him out cold, flat on his back, the camera cuts away to CDR Adama for a second, and when it cuts back, Hotdog is still unconscious, but lying on his side. No one is close enough to him to have turned him over during the quick cut away.
When the Admiral and the President are discussing the Apocalypse she lists all the things that could destroy them, Cylons returning, hurricanes, volcanoes, and she mentions earthquakes, Why would she say the type of quake for a planet they have not reached? She could have said "planet quake", or just quake.
In the Extended Cut (00:21:45) a crew member can be seen walking in the distance behind the Chief and Cally.