I am a little perplexed and feel a little red flag about her having all this information very well organized and immediately available, which seemed weird to me.

I don't feel right demanding they pay when I contributed to them missing a second month by not raising the red flag by noticing I hadn't received that month's rent.

What are the red flags? 

That looks like a big red flag to me.

I've had a Craigslist rental ad up for weeks with no issues, no discriminatory verbiage, etc and since I had a "run in" with a local RE agent who was trying to force me to take her applicant (who was on every program in the book; not that there is anything wrong with that) I believe she is behind the flagging since I wouldn't accept the applicant.  

The pictures look nice, and a drive-by didn't trigger any immediate red flags, but I am budgeting for the worst just to be safe.   2) How would I go about making sure the title is clean?

Those aren't always in the best locations (like next to railroad tracks) and on infill lots typically, but they're out there.Not sure where the MLS is wrong...they're there, but probably agents flagged them wrong somewhere that they don't show up in your search. 

I have been researching the Huntsville market for some time now, and one day I realized that there were a lot of rental listings on Zillow that had been sitting for more than 100 days, which is a red flag to me.

It's tough to say with certainty and it a lot of success in the MTR market hinges upon operating ability, property layout, understanding your clientele and ability to adjust to the market.This article does flag some cities that are good for MTRs: https://www.stessa.com/blog/hot-spots-medium-term-rentals/

You need a house checker to flag any big problems and to plan your spending.