How do you explain a failed inspection to a client when the issue is minor?

You need to have rock solid contracts to set this up well and it needs to be very visible. Then when something fails, it needs to be addressed with a phone call and you need to break the news to them professionally. Let them react - listen to them being frustrated then let them know whatever the consequences of that are. For us, if they didn't give us enough info and we can't do any work, we charge them $250 for the failed visit. I explain this isn't so I make money, in fact I don't make anything on that. It's so I can pay my guys who planned their day around their job and now can't work because they were on the schedule taking the place of another job. Usually hearing the humanity behind it softens the blow. 

I offer my clients a 12 month warranty on my pest control service (rodents) if they agree to have me complete all the exclusion work I recommend. Then I kill off what ever population is in the house and walk away...95% of the time.

If they see activity after 2 weeks that is pretty much me saying I missed something and failed the inspection. It's not my favourite way but its my only way. People are never angry or upset because the current population is going to be lessened, and everyone knows what a persistent mouse can do. I will show up again and make sure I do a good second inspection and ensure nothing was missed. A second pass of the house in the opposite direction or from a different angle does sometimes help anyway.