I believe it tends to give me a slightly lower return, because the sponsor is going to be more careful, and if there is a severe downturn will prevent me from taking catastrophic losses.

I agree with @Nathan G. protect yourself first.For a quick fix, you can get a handyman to board up the window while you wait for insurance or a replacement to prevent damage and safety issues.

Realizing the obvious spending of closing costs, are there other down sides or obstacles preventing me from doing this?

This usually means there's a porch or Florida room that can be brought "under air" to increase the total square footage of a home and drive the price WAY up from the purchase price.Also, and I can't emphasize enough how important this is, put some thought into your design.

It has been well-maintained overall, but has not been updated (knob and tube wiring, radiator heat, no central air, plaster walls).

Was there anything that stood out as a red flag (given hindsight) during booking/screening that could potentially help prevent the same problem from happening again?

I thought of Air bnb yurts on it, building a amphitheater, expanding the farm for livestock. 

The place also has central air which no other places have, they all have window units.

It ended with me spending about 10k out of pocket (I decided to put in central heating and air, instead of replacing window units) and then had to have drywall replaced, refrigerator, and the whole house had to be painted because they locked their dog inside.

The first pillar is avoiding unnecessary and risky activities (don't drink and drive, insurance generally won’t cover your poor decisions) and take good care of your investments(maintain your property, etc) - these simple steps will help you prevent lawsuits before they even occur.