Suppose you have someone designated to identify plumbers, call him Bob. Bob has a public key, and if a plumber, call her Alice, comes to him and proves in the usual meatspace ways that she's a licensed plumber, Bob signs the plumber's public key, along with their name and license number and the date, signature good for a year. Maybe Bob works for the government, maybe he doesn't, but in either case he's a trustworthy guy who genuinely only identifies real plumbers and both the landlords and tenants trust him to do that.
Now the contract says that if the tenant identifies a plumbing issue, the landlord will provide a plumber identified by Bob to have a look at it. So the tenant can sign a statement declaring a plumbing issue and if the landlord doesn't get a signature by an identified plumber saying it's resolved within a given time, the landlord is in breach, verifiable with math. But if the plumber comes and signs a statement that there wasn't a plumbing issue, the errant tenant has to pay their fee for showing up, again verifiable with math.
Then the remaining issue is corrupt plumbers. But you can't solve every problem all at once, so you rely on the state to revoke licenses in demonstrated cases of corruption. Or on Bob to stop authorizing them.