Each rescue works to it's own guidelines, so please bear in mind that my comments reflect only what I would look for, as a volunteer for one particular rescue. Other rescues may have different policies. YMMV.
In a post-placement check, I would hope to see that the dog is settling into the home, that the family demonstrates responsible dog-ownership, that the dog is well cared for.
I can't give a standardized check list, as so much would be geared to the needs of the individual dog. The bonding I'd look for had the owners adopted a well socialized pup would be different than if owners were rehabilitating a dog who had suffered years of abuse. A young border collie requires different physical and mental stimulation than a 15 year old pug does. For many things, there is no right or wrong answer - it's more important to me to see that the owner has made an effort to understand the dog's individual physical, emotional and medical needs, and is making informed decisions.
But some basics, in random order:
Does the dog appear happy, bonded with the owners? Are the family happy, bonded with the dog? I like to watch the general interaction between dog and owner.
If there are children in the house, I'd want to make sure that the adult provides appropriate supervision, that the children behave appropriately with the dog, and understand they must follow the adult's instructions when interacting with the dog.
Training: What kind of training is being done? Are you training on your own, or through a school? Are you using positive, non-coercive methods? If you adopted the dog after 1 Sept 2008, I'd check that the new owners have met (or are taking steps to meet) their obligations under the new law.
House/Garden: At the time of adoption, you would have discussed whether this dog needed a house with private fenced garden, or whether a flat with communal garden (or no garden) was acceptable. I would check that that conditions made at time of adoption are still adhered to.
Physical exercise, mental stimulation: Is the dog getting what he/she needs daily?
Is the diet appropriate to the dog's nutritional needs?
Is the dog receiving appropriate health care?
Spaying/neutering: If not already done by the rescue, you would have likely had a clause in the adoption contract specifying by when the dog must be spayed/neutered. I'd want the proof that it had been done. (If female - males I'd be able to tell.

) If medical grounds contraindicating spaying/neutering have been discovered post adoption, I'd ask for a statement from the vet verifying that.
But the primary focus of the post adoption visit is honestly not to judge (after all, the rescue has already put you through the mill during the pre-adoption check

) but to offer support as you and the dog are getting to know one another.
This is the time to talk about any problems or concerns you might have, and to ask for advice. Every volunteer knows well the ups and downs you go through with a new dog in the family - been there, done that, have laughed and cried ourselves, are more than happy to share experiences, or direct you to sources of help. The rescue is there to support you and your canine family member.
Good luck, don't worry - I'm sure all will go well.