I'd enjoy a damage control mission, where you run around repairing broken consoles and putting out fires with the handy fire extinguisher. This could be a nice addition to boarding party engagements, with engineering and science characters repairing the ship when they're not fighting alongside the tactical officers.
I suppose that this could be used as a death penalty of sorts, with a damage control instance triggering every time your ship is crippled in combat (i.e. hull reduced to zero), but I can see why that would be problematic. It would probably take too long to switch between ground and space instances, for one thing.
Genius! I have posted on a few threads about this. Your idea to have them be a death penalty is just plain awesome. Its sort of a penalty because it slows down your mission progress, but its also a bonus because its awesome. I see no downside to this!
EDIT: You could even give people a choice to either do the mission, thus consuming time; or make them pay a repair fee. This concept is used in WOW, where you have the choice to either find your corpse, or get resurrection sickness.