In the flashback sequence to the CIC of the Battlestar Valkyrie, Commander Adama is wearing admiral's insignia on his collar. He was not promoted to Admiral until many years later.
After Col. Tigh breaks up the fight between Adama and Bulldog, the blood on Adama's chin switches between the left side of his mouth, and the center.
At approx. 42'30'' Colonel Tigh walks in to Admiral Adama's room and you hear the sound of the door closing, we then cut to a shot of Tigh and clearly in the background we see the door only just shutting.