The interior sets used for the Battlestar Pegasus are actually leftover sets from the abortive John Woo remake of "Lost in Space". Woo's series never got off the ground, but its sets were placed in storage. They were then heavily remodeled and reused in this series for all scenes on the Pegasus.
At 8:14 when Cain shakes Adama's hand, she turns her hand counterclockwise to put her hand over his. In body language terms, this is a dominance display. Cain does not do this when shaking Roslin's hand, however.
The Pegasus is a Mercury Class battlestar, with several notable differences from the Galactica. It has four launch bays, smoother hull design, and attendant robots in its bays capable of both fighter repair and manufacture. Also, the landing pods do not have to be retracted prior to FTL jump.
The story for episode #2.10 "Pegasus" is loosely based on the Original Series episode "The Living Legend" which also features the Galactica discovering the Pegasus.
A 59 minute Extended Edition of this episode is included on some commercial releases of Season 2.