I don't know about rescue dogs but I'd be looking to get to know the dog, take it for walks, see it interact with kids, other dogs and see if it responds to some basic commands and shows an ability to learn them.
It is a bit of a lottery as it can be difficult to know just how being in the rescue centre might be effecting the dog, particularly if the dog is new to the centre. You can understand that, for the dog, those first few days/weeks are confusing and stressing - be it frightening or exciting or anywhere in-between. You can only guess how they'll re-act in a more relaxed environment.
Rescue centre are emotionally tough places to visit. You have to be quite steely in your resolve, otherwise you'll adopt just about all of them!