As the Cylons begin transmitting the Cylon virus, there is a shot of the firewall screen showing that the first firewall has been penetrated before it actually happens.
When Gaeta is racing the clock to recalculate the position of the fleet, there's a moment when the bar on his console clearly shows the calculations as 80% complete. A couple of minutes later, there's a cut back to the console, and the calculation is just then flipping from 79 to 80.
Medical Inaccuracy:
As Commander Adama is on the operating table, the paramedic (Layne Ishay) states that his heart has stopped, and you can hear the sound of a flat-line in the background. Unable to use a defibrillator, she asks for a knife. Suddenly, the sound of a flat-line has changed to the sound of normal sinus rhythm without any medical intervention. Even if this takes place in another realm far more advanced than our own, they still use the same medical tactics. There is no way to go from a flat-line to normal sinus with no intervention.
As the paramedic (Layne Ishay) is about to make an incision into Commander Adama, you can clearly see that her incision begins on the border between the thoracic cavity and abdominal cavity. When you see the stitches on Adama after the operation has finished, the incision is seen just below the neck, which is a good 5-6 inches higher than where her incision was shown to be made. That portion of his body was also covered by the gown when her incision was made.
When Kara Thrace finds the Arrow and breaks the glass, in the background is a clearly visible cameraman, wearing a vest and red shirt. He shows twice as camera angle changes.
The whole plot centers around Gaeta's failure to update the fleet's jump coordinates, resulting in Galactica being separated from the fleet. The solution, to network the computers in defiance of Adama's standing policy, is ludicrous. Season 1's "Tigh Me Up, Tigh Me Down" established that strict communications logs were kept, and Adama violated that policy in locating and returning Ellen Tigh to her husband. Logs of all coordinate updates would have been kept, and the coordinates themselves should have been logged for just such an emergency.