Find the area you want to target and have the addresses skipped traced. 

If it’s a TCS then that creates a whole different set of concerns (internet connectivity, available time, etc).

I was thinking about giving each tenant 12 self addressed stamped envelopes to me so they can put the rent check in and send to me.  

Specifically, for me as an investor, if I were NOT licensed there are some smaller multis (2-3 units, the most common type we've got) that have exemptions for protected classes in certain cases, but as an agent you waive all exemptions.Obviously this isn't a big concern, but I've seen it trip people up and it's a hassle if you forget.Good luck!

Anything I should be concerned about? 

There are AGI limitations for contributions, but at $12k I wouldn't be too concerned about that.It may be worth reading IRS Pub 561. 

My concern is, can any city where I purchase a mobile home park randomly decide to change the zoning so the mobile home park is non-conforming and no units can be brought in?  

Feel free to message me the addresses and I can help you make that determination.

My concern is that I catch them up close the deal subject to and the bank still forecloses on the property.

As Margaret says above with distressed sellers this is not an issue but even then their attorneys should be concerned.