A concession like that for a contingency would get some notice.

If they are on month to month when and if I take over they can be given proposer notice by me and hopefully avoid any conflict

As John said, the appraisal not coming in high enough is the most common issue (not that it's very common, I don't want to scare you), but sometimes we can work it to your advantage if it's only off by a small percentage.  

Know your state landlord tenant regulations.I would serve notice and begin the eviction process.

My question to the community is what should I look for in terms of common problems.

However, recently I've started looking around and noticed in my (semi-close) area, there are plots of land for ~70K in semi-rural areas. 

I've never done it, but might make sense to put some notices in the house, taped to a window, the door, a flyer outside or something like that that states....THIS HOUSE IS NOT FOR RENT.....it is only for sale.   

If you don't pay, you get a 10 day notice.

You will notice that there are frequent posters who respond to posts that have these keywords.

You may need to legally do something now in terms of notices.