The house had brand new paint and every thing was functional and very clean at the time of rental.

Now, they have asked us to pay for paint so they can repaint the living room ("the current color was a crappy job", they demand a backsplash in the kitchen....I understand I have repaired more often than what tenants would like but is this ridiculous? 

Solid handrails and steps, lots of good lighting, non-slip treads on stairs, orange paint or tape on low hanging obstacles such as pipes, joists, beams, and wiring.

When I work with flippers as an agent (I also flip myself) I like to be involved so I can point my clients in the right direction as to what finishes to pick, what paint colors to use, to help them choose or avoid what the market demands etc.

Home Depot was there once explaining their "pro buyer" and paint discount programs. 

It is essentially an epoxy paint that wears fairly quickly with heavy use.

May need to check your liability insurance policy for lead based paint & mold exclusions &/or liability limitations.This is another reason we add high pitched sump pump alarms for flooding & in higher end homes the alarm is connected to the security system.

For example, they are making repair request for paint peel (see picture below), and a hole in the vanity board (see pic below).

Any thoughts on a 3rd part painting estimating service to help you get an idea of what a fair price is that you should pay in your area for painting work?

When we went to the property the brand new tiles were scratched, the lighting fixtures were installed wrong, they painted the windows....So maybe if you are going to invest out of state get a move-in ready property!