Plot hole: The General informs the President that the Eastern Alliance has just launched its missiles. But the General has been sitting there throughout Apollo's speech with no communications device. So he couldn't have known that the missiles had been launched.
Factual error: Apollo tells Brenda and the General that he's from another galaxy, and Starbuck later repeats this impossible claim. The series writers have again confused galaxies and solar systems. Intergalactic travel would take thousands of years. The rag-tag fleet usually moves at only sublight speed, and it traverses only star systems, not galaxies.
Plot hole: When Starbuck attempts to liberate Apollo, he captures two guards, saying "Now drop them or I'll incinerate you". They comply and he leads them to a room where Apollo's weapons and equipment are being analyzed. The analyst holds a radio on which we hear Starbuck say "Drop it or I'll incinerate you". First, Starbuck isn't transmitting. Second, he already has the guards disarmed and in custody. Third, the words are not the same as spoken earlier. Fourth, there's no reason such a transmission would have been delayed when sent radio-to-radio.
Plot hole: The President and the General argue on a podium in front of a large gathering of citizens that are seated all around. When the General is told that their enemies have launched an all-out missile attack that will trigger their own automated response, wiping out both sides in the next six minutes, the audience is completely motionless and doesn't appear to react at all. They take the news that they are all going to die remarkably well.