Nice article.
Tooearly - Homecheckers are NOT interested in wiping fingers along surfaces to check for dust!
They will want to know if your garden is secure and the property is safe for a dog. They will ask you if you own or rent - if you rent, please be prepared to show written evidence that your landlord allows pets. No reputable rescue will rehome to a tenant who cannot prove this.
They will want to meet all adults who live in the house (even if they are not related to you), and will want to know the ages, sex and any special characteristics of the children who live there. They will also want to meet any existing pets. They will probably ask you about allergies or other health concerns. They will want to know your lifestyle and working patterns, and what arrangements are being made for exercising the dog. If you are going to use a dogwalker they will probably want to meet them.
Piles of washing won't be a worry, but for instance, heaps of food, or dirty dishes, MIGHT be a red flag depending on context - they would want to know for instance that your dog could not gain access to your child's chocolate dessert or raisins (as both chocolate and raisins are poisonous to dogs, and often found in people's homes). Some dogs, greyhounds for instance, are easily capable of "counter surfing" so the homechecker will need to be aware of how you might manage that.
Reassuringly, if a house is incredibly tidy with perfect white carpets and cream coloured sofas, then the homechecker will want to make sure the adopter will really be able to adapt to the hair, mud and general oomska that comes with dog ownership.
Much of the homecheck will be about talking to you about your understanding of dog ownership and your expectations. Finding out about your experience with dogs, why you have chosen a particular breed (if applicable), how the dog is going to fit into your lifestyle and what your expectations are. You should feel comfortable with your homechecker, and you should also use the opportunity to check the rescue out. Ask lots of questions, about how dogs are assessed before adoption, how they are matched to a particular home, what advice is given on settling in, early training, feeding, and ongoing aftercare/support. They should also be able to tell you about the fun things that the rescue do/organise such as social events, dog walks, charity dog shows, activities etc.
Finally, they should walk you through the adoption process, explain what they are going to do after the appointment, and give you clear timescales and outlines of what will happen next to progress the adoption.
Good luck!