AutoEurope's website says the drop off at Granada airport is not open on Sundays (our day to unload the car!). Should I have concerns about not having someone inspect car? I've seen some posts here about companies saying the car was damaged and charging for damage. If there is no face to face with the car rental agent how can you be sure both parties are satisfied? Any suggestions to ensure they won't rip me off?

I did same at Jerez airport. Had no problems.
If you want some proof, take a couple of pictures (inside/outside) of the car before you drop off the key.

I would add that you should save gas receipts showing you left the tank full. In addition, save receipts showing your whereabouts the several days following drop off. I say that because several years ago we dropped a car at a location that was staffed but who would not give us any kind of receipt. In a hurry to catch our train, we left without anything to prove we had returned the car. Sure enough, we received charges for 3 extra days. Apparently, the attendant decided to use the car over the week-end and charge it to us. After 6 or 8 months the problem was finally resolved through Auto Europe because we had receipts showing that we were in another country the three days in question.

Another time at Frankfurt, we turned in a car at the airport before the office opened and didn't have any trouble at all.

More recently, when we dropped a car at CDG, we were told we didn't need an inspection or receipt. Although we finally did get the inspection okayed and a receipt, it seems to be the trend to do neither.

Just take photos and save all receipts.

We have rented numerous times in Europe and I don't think our car has EVER been inspected on its return. It's always been drop the keys and wave goodbye (often times the offices are closed). But we always rent though Avis - maybe it is different with other agencies?

Thanks for responses. Good idea to take photos (with date stamp I should think) and keep gas receipts. These are the details that make me crazy before I go on a trip!

Make sure the Granada location has a drop box. Sounds weird, but I once returned a car to a location where there was no box to leave the keys and insurance package. So I took them with me and the next day went to a Post Office and sent them back with a note. I called the rental outfit the next day too, and they said "Why didn't you just leave them at the cafe across the street?"

HUH? I got charged for two extra days.