I am soon to be in the same boat as you.. I am getting a new job and will be travelling for weeks at a time.. my partner is gone over 10 hours a day, so I will soon need a dog walker.. It's so hard to find because I don't trust anyone with my dogs except me and my partner!
I would have the potential walker over to your house to see how they interact with the dogs.. I dont know specific questions to ask, but i'm sure just by talking to them you can get a feel for if you trust them or not.. I would explain specific behaviors of my dogs that would be important for them to know (like if they go crazy when they see a small animal like a squirrel) and see how they respond.. Mine are very prey driven, so I get nervous with strangers walking them, Diego can pull your arm off when he wants to chase a rabbit!
But I think the #1 concern would be can you trust them with your dogs, and do your dogs seem to get along with them.. Good luck in your search!