@Ashton A. Moore
I see. I really think the other stuff on your list is extremely negligible. Assuming your inspector did his job and he didn't miss anything major, this (and maybe the moisture) would be the only things I'd want to have looked into. If you are happy with the deal otherwise, I'd just get an HVAC company over there for an inspection (should be reasonable), explain the situation, and ask them to verify correct installation of the unit, etc. If everything but the intake checked out, I'd ask them (or your handyman on the other little jobs) if you can give them an extra $50-100 bucks to make a cheap, screw-in plate of some sort for the filter. They'd be making a tidy profit at that price, imo. It should take 5 minutes and $3-5 for them.
I find the intake/filter thing VERY odd. Especially for a new unit. I'd be way more concerned about larger issues with the system. If there aren't any, I think getting a filter on that thing is a chip shot. You could honestly even make it look decent if you cared enough to.
If you proceed, I'd love an update. You've got my curiosity.
Best wishes!