During Starbuck's first combat, the moment after her viper is shot, her helmet is incorrectly sealed.
At 57:33 Boomer's Raptor is hit by shrapnel after the Cylon missile hits their decoy. The Raptor's hull is breached, and Helo puts a patch on the hole in the floor, stopping the air leak. Problem: whether the patch worked by suction or was magnetic, the diamond plate texture on the floor would have prevented a full seal, and the Raptor would have continued to lose air until the breach was repaired. Despite the air loss, Boomer does not replace her helmet when the Raptor lifts off at 1:19:44, and still has it off at 1:35:30, when she should be rationing air for the passengers and ensuring she still has air to pilot the ship.
While approaching Caprica, Boomer states that they have enough inertia to reach the planet, with the Raptor shut down. The correct term would have been momentum, or kinetic energy.
At 1:51, the officer at the armistice station reviews a fact sheet about the Cylons. The word "centurion" is misspelled as "centurian." At 27:43, the word is correctly spelled in the display in the Galactica museum in the starboard hangar pod.
While conducting the press tour, Doral refers to the ship as the "world-famous" Battlestar Galactica. Considering that the colonies include at least twelve inhabited worlds, he should have said "worlds-famous" or something similar.
In the opening credits, "Production Designer Richard Hudolin" appears as "Prduction".
Commander Adama says "Oh, Jesus" once. The colonials are polytheists and worship the "ancient Greek" gods.
When Laura Roslin is taking the oath of office, the priest asks her to repeat after her. When the priest says, "that I take the office of the President of the Twelve Colonies of Kobol...", to which she responds "that I ACCEPT the office of the President of the Twelve Colonies of Kobol..."