I do not accept tenants that smoke.  

If the seller had some basic understanding of financing, they would realize why they should not accept it without substantially raising the selling price.

I don't know of a legal prohibition on it, but you would need to find a settlement company willing to accept it.

By listing and accepting bookings year round for the first year doesn’t take away your ability to occupy the property when you want to.

You signed the lease and accepted payment, which makes it a legally binding agreement.

Hopefully, if that situation arises, the notice results in attitude correction and the lease can continue uninterrupted.Having said that, if the eviction is 5 years ago, I'd probably accept the couple - but let them know I'll be keeping them on a short leash.

Or increase the threshold or requirements for accepting a tenant to avoid risk of evictions? 

Brokering a property isn't just about getting an acceptable offer for the seller.

Hi, I am new investor and just got my first cash offer accepted for an investment property which I am planning to use for a long term rental.

I told him he might as well accept it as it is or go back to Florida as that's just the culture.