When the Galactica is preparing to do its first FTL jump, the hangers are retracted into the ship. As the ship is jumping, however, the hangers are fully extended again.
Adama takes his glasses off twice when first contacting Apollo on Colonial One.
When Apollo shoots the missile and loses power, you get a shot of the Viper MK II Cockpit when he pulls the trigger, however when he loses power,it shows a Viper MK VII cockpit losing power.
The floor of the starboard landing bay during the decommissioning ceremony changes from the standard runway in wide shots to the red walkway lines of the hangar bay.
Just as Boomer brings in the fuel ship to the civilian fleet, there is a brief external view (at around 1h 55 mins) which shows three Viper Mk VII's flying in formation from right to left. The only Viper available was Apollo's, and it was disabled in the cargo bay of Colonial One.
During the first scene on Galactica, when the camera follows Starbuck through the halls, a man she passes makes room for her and can clearly be seen looking towards the camera crew and waiting an extra moment for them to pass, even when Starbuck is well out of the way.
During the first FTL jump the countdown of 10 seconds lasts around 25-26 seconds.
In part 2, when the fleet is preparing to leave the storm at Ragnar station, Col. Tigh is heard giving orders to lay down covering fire, but his mouth isn't moving while he speaks into the radio.
At 0:57 when the shuttle is attacked by two missiles Bodi says the missile is locked now, but the missile was already following the shuttle which wouldn't be possible if it wasn't locked.
Originally, the Colonies were to be twelve lands on one planet, but this changed and they became twelve different worlds. When Adama asks Tyrol where they found his Viper Mar II, Tyrol said it was "in Sagittarion" where he should have said "on Sagittarion."
The Colonials have a polytheistic religion and throughout the series say "Oh my Gods," yet Adama says "Oh my God" when he sees his old Vioer and the CAG says it when the Cylon nukes are approaching.