Revealing mistake: Just after Tigh announces that Centurions will be "pouring in at platoon strength", the next shot shows those Centurions marching though the Galactica's halls. None of them are casting shadows despite the various nearby light sources that should be causing such shadows. This is most obvious looking at their feet.
Continuity mistake: Near the end of the 4th season episode "The Oath", Adama and Tigh choose to stay and fight rather than flee Galactica with Roslin. Apollo is not shown voicing any opposition to this. Yet in the next episode's opening, he is shown confronting his father, saying "No, Dad, you can't stay here". While this moment can be excused as having happened off-camera as the mutineers were shown approaching in the prior episode, it is the later show's narration which states "Previously on Battlestar Galactica" that is technically incorrect.