Put a table over the trailer hitch, in my mind the inspector should appreciate that, it could be his shin. As far as the cords, I would think that they are looking at tripping hazards for you, customers and passer bys, no cords just laying on the ground. If you can get away without your inverter while the inspector is doing his job, leave it in the car. Break it back out when he leaves and just make sure that all is safe for you and your customers.
Safety is the main issue here, both your food and your surroundings.