I have 2 rescues. I've found that with rescues sometimes things don't work out for some reason or another. With my first rescue Max, he chose us so it seemed that we didn't have much of a choice
I chose Lily from another rescue and with her being a puppy mill rescue, I was scared for genetic disorders. So far she has a clean bill of health. Unfortunately I don't think that rescue groups usually don't check for genetic issues unless of course the dog is sick when they get them. They do get vet care and are released to a home when they are stable. With both of my rescues, I took them to a vet right away to get checked out, but I didn't do any blood work to check for genetic disorders. My thought was that if I'm going the "rescue" route, that I would take on any issues as they come. Its sort of a risk I guess, but it was important for me to adopt. Unless they were a surrender from a previous owner, they don't come with a health history and most times even their age is an estimate.