The only required RV inspections I know of around here is a yearly State safety inspection required by DOT. We have that here in Virginia and the trailer has to display an valid safety inspection sticker just like the Truck Does. What triggers this in Virginia is if the trailer has electric brakes then it requires a safety inspection. I'm sure there is a weight thing as well but not familiar with what is...
The safety inspection only involves the tires, brakes, wheel bearings, and trailer lights. I have never had to demonstrate that the electric brakes work but they always pull a wheel and look at the brake pads...
Roy Ken