Seriously, though, I didn't see an issue with his tone. It sounded more incredulous than disrespectful.
I have relatives who now or in the past have worked in mosdei chinuch: school secretaries, head of seminary, executive director, yeshiva dean, principal, rosh yeshiva, rosh kollel, maybe a few I'm forgetting. I can imagine their response in this situation.
Instead of:
"You're the one writing a summons, so you must know something I don't know. Which way do you want to go?"
I can imagine them saying:
"Maybe there's some mistake? Our school is actually closed to students now. Come, let me show you around. Usually you'd hear 300 kids here, but sadly the classrooms are quiet. We recently renovated our auditorium, I'd love to show it to you."
Instead of:
"I have to record you, because you give me a summons outside. How can I not record you?"
I can imagine them saying:
"You may be concerned that your boss won't believe that the classrooms are empty. Feel free to record what you see here."
Instead of:
"It seems like you guys have a list, that you just go around giving summons to.."
They would not feel the need to accuse an inspector of doing the job she's been assigned. That can be taken up with the mayor or the courts.
And there would undoubtedly be empathy with a government employee working out of the office, with an offer of a hot cup of coffee and a chance to use the restroom.
He was very polite cut the nonsense
And they wouldn't consider "cut the nonsense" to be very polite.
But, of course, being able to communicate effectively is part of the reason they got their jobs.