Factual error: Apollo tells Boxey they're leaving their star system and entering "a whole new galaxy." Wrong. Throughout this episode, the writer confuses solar/star systems and galaxies, which are vastly (literally) different things. Even with hundreds-of-times-faster-than-light drives, Galactica's fleet would need thousands of years to cross between galaxies.
Revealing mistake: When Apollo fires at Robber, his shot hits a pillar, knocking a chunk of it off. As he runs behind the pillar, a circular device dangles from a wire in the damaged part of the pillar- the remnants of the effects charge that was used to cause the damage.
Other mistake: The very first shot of the episode shows the Galactica is coming through a cloud of "asteroid dust". The ship is intermittently obscured by the black dust, yet the stars in the background remain perfectly visible- barely a flicker as the dust passes through the shot.
Continuity mistake: When Apollo asks Adama if he was ever like Boxey, Adama replies "Worse". The two characters are standing well apart, each leaning forward with both hands on a railing, shown from the front. When the shot changes to show them from behind, Adama has his arm around Apollo, hand on his shoulder.
Continuity mistake: In "Saga of a Star World", it's established that the Cylons are entirely robotic. Their creators, a reptilian race also known as Cylons, were made extinct by their robots millennia ago. Yet, when Omega reports that life signs have been detected, Apollo asks "Cylons?". Apollo is the character that previously explained their history, so he knows Cylons aren't life forms.
Revealing mistake: Starbuck is romancing both Cassie and Athena in different rooms aboard the Rising Star. Odd that both rooms have the same wrinkle and tear in the wallpaper just under the window. There's also, in both rooms, what looks like a black thumbtack repairing the glitch.