Deliberate mistake: When the Vipers make visual contact with the attacking Cylons, an exterior shot shows a large group of Cylon fighters from the front/right as they drop into view and move left to right. The rearmost ship on the left is a gold color while the rest are the usual gray. This odd effect is also seen in the first episode's first battle as well as during the last episode's last battle- an odd coincidence. The original concept for the show was to have these gold ships be the squandron leader, but showing it every week would be too expensive, so that idea was dumped and the one shot with it got used a few times without explanation.
Continuity mistake: After the big battle, Apollo announces that the Cylons are "on the run". Adama orders all the Vipers back on board Galactica, and when they've landed, he is informed that two are missing. Apollo and Starbuck have headed off to find the Cylon base ship on which a Cylon reports to the Imperious Leader that an attack is imminent. When the leader suggests that their Cylon Raiders can defend them, the Cylon replies that the Raiders are still engaging Galactica- but this hasn't been true for sometime- that battle is over.
Deliberate mistake: When Starbuck and Apollo attack the 'flank missile launchers' of the two Cylon base stars, the shots of the launchers exploding are actually of the laser cannons on the Galactica (note the red horizontal striping on the "wall" behind each cannon).
Plot hole: Galactica's sensors detect a second Battlestar, Pegasus- a shock to everyone aboard. Then its commander, Cain, speaks with Adama via video hookup, and announces that he'll be arriving at Galactica momentarily. Yet he arrives in a Galactica shuttle, marked "GAL 356", which hasn't been sent to go get him since they only just now discovered Pegasus exists. Even worse, this is the same shuttle destroyed several episodes ago when it crashed on Ice Planet Zero.
Revealing mistake: When one of the Nomen throws his "boles" at a support column, it is obvious in the side shot that the actor never really lets them go, but just turns his hand to block sight of them as his hand drops. The glow can be seen traveling downward, despite the next shot showing the lighted weapon traveling forward.
Plot hole: Apollo takes Adama down to the surface of Caprica aboard his Viper, yet the Viper is a single-seat fighter. This is the only time the single-seat craft is used to carry two people (though there is no shot of the two aboard- it is simply shown landed with the two characters nearby).
Continuity mistake: When Apollo asks Zac, "How many of them can you make out?", Zac looks at his targeting screen and replies, "Four." However, the screen displays five. The ensuing battle proves Zach is correct with four, meaning the film makers inserted an incorrect targeting screen graphic.
Plot hole: Considering Galactica's mission of protecting the entire fleet, she wouldn't risk having recruits brought aboard that haven't been through a security screening already, especially a pair from a known warrior-like race, both of whom are wearing weapons openly. Nor would they be guarded by a crewman who willingly answers classified questions about locations of decorated Warriors posed by total strangers. Yet all of these gross security oversights occur in this one episode.
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.
Continuity mistake: When three Vipers land on a planet, the pilots emerge and discuss how odd everything looks in the strange lighting of this world. The colors of these shots have been altered so that grass and other green plants look red, and the red stripes of the Vipers look a yellowish green. Naturally, this has made the pilots look a bit odd, too. But when the scene changes to an area devoid of living plants, the colors return to normal Earth-like hues- as if this world's sun has suddenly changed its attributes.
Continuity mistake: During the wedding ceremony, Adama states he is about to recite the most powerful words in the universe. He then says "Under the eyes of God, bound by the symbol of the faiths of the Lord of Kobol.". But in doing so, the actor forgot that in the show's "universe", humans believe in multiple gods, referring to them as the "Lords of Kobol" and "The Gods".
Continuity mistake: While on patrol, Apollo enters a void in space, where no stars or other navigational fixes are visible. But in at least one shot, his ship is shown from the left side with stars in the background. It's the shot immediately after Adama says, "That's odd."
Continuity mistake: When the Vipers come to Galactica's rescue, an interior shot shows a pilot hitting the 'Turbo' button. The next exterior shot shows two Vipers pulling upward as we hear the familiar sound of the Turbos- but no white exhaust is emitted by these two Vipers as normally seen when Turbo is used. Seconds later in the same shot, the sound is heard again as two more Vipers turn right, but they do display the white exhaust effect.
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.