Some sort of hub world would be cool- may it be a tavern area to walk in, a port, or a large ship.
Customization of ships beyond simply picking guns would be awesome, too, i.e. earning different types of system properties, like stronger balloon with slower up/down movement.
If the adventure mode was something like the Rebels vs the Loyalists, that could carry over into weapon types and teams to push along a plot, unlike something like Unreal Tournament, which had teams, but didn't impact the story at all due to its nature of 'kill things for 5 minutes'.
A.i. pilots would be nice, too, so each mission wasn't simply -fly here and let the AI do the work for you-, or so you don't have to triple up duties, anyway.
Adventure rewards could give prizes, or in-game currency for extraneous ship parts, decals, cosmetics or even buying smarter-A.I. crewmen for further missions(training or something). The cosmetics and money could carry over to online... but it doesn't matter too much.
If the adventure mode had specific missions and not simply Deathmatch after KotH after Team Deathmatch, each one could have specific conditions or challenges involved, like no spyglass use, less crew, permanent half-power systems, don't get marked by spyglasses by hiding in cloud cover to reach a target, enemies have extra resistance to damage types and specific weak points, etc etc etc.
If anything, I'd just like if the adventure mode was challenging enough to make me feel good about overcoming its obstacles- not simply going through the motions to win prizes. With a game like this, its adventure mode could act like a great way to challenge veterans and train new recruits new tips and skills.
