I work at a boarding facility (also a vet clinic, so the we aren't the main priority) and so I know how things are done. My main concerns when boarding my own dogs would be:
1.) interactions with other dogs. This can be as simple as having a kennel with fencing that allows the dogs to see/interact with one another while caged (even if that is just chain link fencing on the top part of the kennel or a gap in the physical barrier between kennels). My dogs don't get along with strange dogs. Not everyone's dog gets along with other dogs. I don't want my dog becoming stressed trying to get at another dog, nor do I want someone else's dog barking constantly at mine. In at work we know which dogs fence fight and which one's are okay so we space them out accordingly, but it still can't be fun for that sane dog to be barked at all day long by the big aggressive coonhound in the cage next door. We don't offer dog/dog playtime unless they are in the same family and/or close friends specify it, so we don't have to deal with the hassle of interactions gone wrong, especially since we get in so many touchy dogs.
2.) Cleanliness. I don't want to smell feces or urine when I walk back into the kennels and if a dog has an accident, I expect it to be cleaned promptly with proper disinfecting techniques. Yes, it sucks having to clean up after so many dogs...but if it isn't getting done, then you either have lazy staff or not the right staff/dog ratio and that isn't fair for anyone involved. And if a dog craps on its self eight times a day due to being an idiot, then it still needs to be cleaned up after and the dog itself needs to be rinsed off.
3.) Staff/dog interactions. My dogs aren't everyone's best buddy, especially if you are a large male. I don't want someone handling my dogs that doesn't know the first thing about dogs. I don't want someone playing with my dogs that doesn't know how to keep them calm and not rev them up to the point they get overstimulated and start nipping. Actually, after seeing how some coworkers of mine play with and handle dogs, unless I see you interact with my animal first, I'd rather you just not interact with it at all. It isn't that they are mean or abusive towards the animals...they just don't know dog body language. I had my girl Chloe try to bite my ex-manager after he "tried to make friends with her" by going into her kennel (while she was undoubtedly standing tense), squatting down getting into her face, and then running his hands all over her body. She went after him and when he told me what she did, I said, "Well, yah. Duh." And another ex-coworker of mine was so overbearing with the dogs (just her personality) she would scare the more submissive animals peeless (literally) and would cause the more aggressive animals to take offense and try to attack her.
Run size, exercise opportunities, willingness to follow "stupid" instructions regarding food/toys/beds/whatever, and security of the facility is also all important.
Er... bite me. Idiot cage cleaner got a friends toy fox terrier killed by a german shepherd years ago by cleaning two cages at once and I have been turned off since then. And we have signs up every once in a while out here for dogs missing from kennels. 