And if there was, I'm pretty sure that insurance bought *after* a problem starts would exclude that pre-existing problem from coverage.

I've been leaning more towards buying a multi-unit in a rapidly appreciating area vs. a single family home in the area that we currently live in (a suburb with a great school district and is appreciating, but taxes are high), with the idea that the rents on the property we buy (say $5k total in rents) would exceed the rent that we are paying (say $2500 rent).I'm totally excluding any tax benefits/liabilities for this scenario and am purely looking at it from a monthly payment perspective.

You can absolutely limit people from smoking in your apt. and you can exclude any kind of animal/pet. 

Don't be stupid by on-boarding everyone you come across but also don't be stupid by excluding perfectly fine opportunities (= good tenants) simply because they don't have a W-2 (there was another thread about a trust kiddy; I'd jump on that immediately if it were me in the context of financial security - but the kid of course needs to otherwise be a viable tenant, which, uhm, sometimes can be the main issue ;-) ).So with retired folks we as landlords actually are in an even better position when looking at "job security": you can't get fired from your retiree "job"!

I checked with my insurer already and they don't exclude certain dog breeds for landlord policies because the tenant is treated as my customer, which I guess makes me responsible.  

Question: Can I offer electronic payment, cash, or money orders/cashier's checks (but exclude personal checks), to make it more difficult for the tenant to pay with paper instruments?

i have specific requirements which excludes felonies.

We do have a brand new (few years old)  low income apt complex in the area that rents a 3/2 for $700, but I'm assuming I'd exclude that from the comparable properties for rental prices, since mine are single family homes (I know I exclude then for sales price, so I would assume also exclude them for comparing rents). 

I can leave them if youd like but I will not repair them when they fail and they are specifically excluded from the lease."

I had not considered that it might be illegal to exclude or require a particular type of payment.