Small gardens are fine, often the biggest problem I had when home checking with gardens was the bigger ones as once they get past a certain size they tend not to be secure.
Safety is the priority, so it's not really about cleanliness unless it's a hazard eg. Having piles of stuff everywhere that the dog is likely to wreck or harm themselves on.
Home checking is about helping the matchmaking process by gathering as much information about the home that a dog Is going into. We can then pair the right dog up with the right home. It's very rarely about outright failing if that makes sense. Sometimes I have said that it's unlikely that we are going to get a dog that fits into certain homes, and not agree certain matches
I'd encourage honesty because it let's them see what the dog is going to be doing. Eg. If your dog sleeps on the bed, tell them or don't feel like you have to pick up all the toys if actually normally there's toys on the floor so it's important that you have a dog that can leave them be.
Here's somethings I'd be thinking about
Location- eg is it in a quiet rural area, or in a suburban area where they might be able to hear alot of door slamming etc. Is it somewhere where a barky dog would impact neighbours, or where a prey driven dog would be surrounded by 900 neigbourhood cats. Some dogs might need access to quieter walks so a city environment isn't right
Outside space- are gardens secure and how secure? What does the garden offer? Some dogs need a big space to run around in, others just need a spot to wee in and sunbathe. Greyhounds are a fantastic example of the different garden needs. Some are snoozy and could live with limited out door space, others are young and need space to run about in. Some will need very secure gardens, and any passing neighbourhood cat is in trouble. Others can have regular fencing and aren't bothered by seeing and hearing neighbours. Is there a barking dog next door so you would need a dog with no barrier frustration
Other pets. It allows a quick review of your pet. Is it a calm dog that is looking for a nap buddy or one that's looking for someone to play with 24/7 . Will your dog need a respectful dog, or can it put up with a puppy? Some dogs need a calming dog that will build confidence. Others would ne perfectly happy with a neurotic play mate. What's the current dogs routine and how will a new dog fit in? Is there space to separate?
Household members
A home check is normally the longest time we spend with people so it allows us to get a sense of their experience levels, what's important to them etc. You'd be amazed at the amount of homechecks where family isn't on board. Are the kids quiet who'd want a quiet dog, or rowdy who want a running mate. Would they respect a dogs boundaries
General feel of the home
How would a dog fit in here? What are they willing to change to accommodate a dog and what's a non negotiable.
Routines
What are the local walks like? How long is the dog left? What will the dogs daily routine look like? Who is coming in and out of the house? Do you need a dog that's good in the car?
It also allows for a general chat and to be really clear about what your expectations are for the dog. Eg is your family looking for a nice calm dog to snuggle on the couch or a really bouncy dog to play ball with.
Sometimes people tell us what they think we want to hear so a home check allows us to check if you really do have the experience and set up for a reactive dog or if you're better off waiting for an "easier" dog.
It really is about matching a dog and home. What works for some dogs, won't work for the next so having enough information to pair you up.