Here are some minor features that I have come to enjoy:
On-site check-in (either through an on-site management company or a lockbox at the house).
Damage deposit via credit card hold rather than a prepayment that has to be refunded.
A pool area with a bit of privacy (either a privacy fence or facing a conservation area.)
A pool area that has both sun for my wife and shade for me.
High-speed internet (even if for an extra fee: I just want to have it.)
Personally, I don't mind paying by check if the owner is established and we have a good rapport. I particularly don't mind if the check goes to the management company instead of the owner. But, I can understand why someone would want the protection that a CC payment provides.
I do check the recorded deedholder, too. That's good advice.