Continuity mistake: In a wide shot, Apollo is inspecting an air rifle. As the wide shot ends, he holds the rifle wrapped by both hands. When the close-up shot starts, the gun is on its side, held by his right hand while his left is removing the air cartridge.
Audio problem: As Apollo's Viper is under attack by several Cylon Raiders, he radios Galactica, saying "Galactica, Recon Probe 3. Where's Blue Squadron? I'm running out of time." A few shots later, aboard Galactica, we hear Apollo's voice over the radio, saying "Where's Blue Squadron? I'm running out of time." twice, back-to-back. It's a reuse of the audio from the earlier scene. We hear the exact same audio a total of three times in less than 45 seconds.
Continuity mistake: Apollo and Vella sit in front of the fire and she tells him about her late husband. In the two-shots, their shoulders are touching. But in all the close-ups, it's apparent that they're much farther apart and turned to face each other rather than sitting side by side.