After climbing aboard the airship at the start of Chapter 3, head to the Engine Room area and you’ll find four new chests. Head to the Cabin after that, then feel free to buy some Hi-Potions from Barkeep. Also opt to rest in the beds for another 100%-critical scene. That’s about it for side stuff.
Return to the bridge and, near Shinra, you’ll see a CommSphere. Essentially, these allow you to communicate with Shinra while on a mission: just go to the proper part of the proper area to place them. After speaking with Shinra, three Hotspots will appear in which to place the CommSpheres. We’re not ready to bother with them, yet, since there are so many other places to visit, after all.