Mission abort score penalty is (always? haven't checked everything) lower than despawn score penalty. The latter you can see when you click on a mission marker, so if it looks bad, it's worth trying to go there even if you're certain you won't be able to do the mission. If the despawn score is peanuts, go ahead and ignore it if you wish.
Civilian deaths do skew this calculus a bit.
AFAIK, 'case is not closed' is just a string - there's no general mechanic for continuing the 'case'. While theoretically, one could do this on a mission-by-mission basis, I don't recall anything like that existing in the mod.