Uh, hello, figured if I wanted ideas added, I'd have to join up for it.
Let's see, random missions....
Storming a Humanist rally, where there are several human civilians, preferably unarmed or mostly unarmed if you want us on our toes, a bunch of Activists, several Soldiers, and either a few Instructors or a Leader, in an open area with a stage set up. Ideally the citizens would be safely ignored, but anyone actively aligned with the Humanists would have to be taken down to win. It would be fun if there was a chance of your ship randomly being right in the middle of the stage with a dead Leader corpse right in front of it, I can see it now: the leader is right at the height of his rant, spittle flying and mustache sitting proudly on his face, when suddenly, he hears a loud noise. Looking up, he sees a skybus appear out of nowhere hurtling towards the stage, obviously someone lost control of it. He doesn't even have time to scream.
Raiding a church, easily hidden weapons only 2x1 or smaller, and as long as no one shoots a gun or gets seen in employee only areas (marked with red carpet or something), they will ignore your hands. attract notice, by shooting or getting shot at, or being seen in forbidden areas and not silencing the viewer in one turn, and you now have a time limit as well as having people shooting at you. Morale would probably still go down as usual, so high bravery would probably be useful here.
Getting attacked by and attacking Molemen (seriously, where are the molemen?). Figuring out how to force their giant drill subs to surface or noticing a place they're scavenging for gear and attacking, having them randomly run into your base, assaulting an enemy hideout and having them accidentally attacking at the same time (three way battle!). Maybe add some underground dinosaurs, lizard folk and sexy savages too, for the real Hollow Earth scenario.
Later in the game I could see raiding a Spartan Fort, could maybe 'liberate' the womenfolk. Can't imagine it being easy, as they're too paranoid to send everyone off on a pogrom.
On a sillier note, maybe missions to kidnap a musician, who would totally not be Elvis, which could get you involved in
The Cult of the Sequined King(tm). Elvis clones and impersonators would be amusing, maybe the cloning tech could be used to speed up healing?
This got just a bit out of hand, hopefully some of these ideas are either usable or remotely good.
Cheers!