Looking underneath my gutter, I noticed that the soffit is a bit discolored looking. Looks kind of like mildew or moisture marks. Does this just need some tender-loving-care or do I have a more serious structural problem on my hands with my gutter or under-roof ventilation?
A lot depends upon where you are. Here in the great Pacific Northwest moisture is a constant problem: Moss and mildew on roofs, other parts, like your gutters, etc. I even was driving with a friend and he asked:"what's that green stuff in the middle of the road (chip seal surface), and I said, oh, that's just moss. Another co-worker who moved here from out of state asked me was this stuff growing in his lawn was, again, I said, just just moss, but you'd better treat it or you won't have any grass left.
OK, enough of the chit-chat. To answer your question, there are companies here that do a mild beach based power wash on roofs, not a pressure wash because that can be too damaging. They rake off the worst of the moss then treat it with the specialized bleach solution. I've had it done to my house and it cleared up the remaining moss and mildew. It's been great for 2 years now. Gutters, since they are metal, are pretty safe to pressure wash, if you want to do it yourself, but I'd be super careful about not getting any water into the eve vents. The last thing you'd want to do is introduce water into your attic.
IMHO I think you'd be fine with a relatively low power pressure washer to clean up the gutters.....again, just don't put any of it the attic! LOL
One more thing, there are commonly available cleaning solutions that are VERY effective. Just search Home Depot or Lowes. Product recommendations are considered Off Topic here, so I'm not going to make a recommendation. You could use a back pack sprayer to carefully apply the solution. Again, make sure any plants/landscaping is protected.
Lastly if you decide to go with the bleach based power wash, be there to monitor and be sure the company covers all landscaping with plastic and any outdoor furniture needs to be moved where it can't get any over spray or cover with plastic tarp as well.