In the scene where original Kelly & Claire are talking in her quarters, they are drinking from rainbow-coloured drinks. The level in the top of Kelly's drinking raises & lowers between shots.
In the opening shot the shape of the windows changes when viewed from inside the ship.
When Captain Mercer is called to the bridge in the middle of the night to deal with the approaching Kaylon ships, he assembles the senior staff, including Gordon (helmsman) and Talla (security/tactical officer). While it makes some sense to bring in Kelly (first officer) and Bortus (second officer) to assist in making command decisions, there would already be a helmsman and tactical officer on duty as part of the night shift.