During the initial attack on the Colonial fleet, a Cylon fighter disappears without being shot at and destroyed by the Colonials.
When the Cylons begin their attack on the Galactica, Adama is seen wearing his long dress coat over his uniform as he orders "positive shield now!" But in the clip before and the next clip of him afterwards, both while he's still on the bridge, he's not wearing it. The shot of him in it was reused footage from the pilot episode.
At around 15 mins into the episode, the scene where Cain asks Apollo and Starbuck if they know Cassiopeia is out of sequence and was obviously a part of their earlier first scene together on the Pegasus. However it was edited into the episode after Cain, Apollo and Starbuck had already gone to the Galactica, yet here they are on the Pegasus again for no reason.
Because the fleet is running out of fuel, Adama orders the fleet to a dead stop, exactly the wrong thing to do. It takes as much fuel to slow a spacecraft as it does to accelerate to speed. To save fuel he should have just ordered the fleet to shut down their engines and "coast".
As Commander Cain's shuttle approaches Galactica's landing bay the writing on the side of the shuttle is GAL 356 making it from Galactica, not Pegasus. Reused footage.
In "The Living Legend Part 1", the first few laser bolts fired by Sheba are blue, instead of the more usual orange. (This view was originally of two Vipers under fire from CYLON fighters.)
As the Pegasus heads towards Baltar's fighter, the shadow of somebody placing a cloth cover over something can be seen on the cockpit wall behind Baltar.
There was no reason for Apollo and Starbuck to return to the Galactica aboard Cain's shuttle when it would mean leaving their vipers on the Pegasus (and making an unnecessary trip back there to get them).
In the opening scene, it is completely implausible for Apollo and Starbuck to be in a dogfight with Sheba and Bojay. First of all, none of the four vipers would have enemy transponder signals (if any at all) or any other kind of enemy readings, or be making enemy radio signals, and the ships are visibly clear to each other when the firing starts.
If the Pegasus has had the Cylons "on their knees in this quadrant with just one Battlestar," as Cain says, then how could Baltar and his Cylon crew be taken by surprise when the Pegasus appears? Surely Cylon leadership would have alerted the rest of the fleet and their command structure about another Battlestar waging war on them above the planet Gamoray.