I never signed off on any inspection. I filled out financing paperwork and the truck didn't come from the other dealership until I was out of town for a week. When I got back in town that is when I went to the dealership and the salesman wasn't on site and on the phone told me to drive away with it. No inspection with me and no signature to take ownership.
I just got off the phone with the manager who clarified it is not an option to get another truck from another dealership, it is not an option to order a new truck, it is not an option to cancel financing. Apparently as soon as I filled out financing paperwork, they submitted it to FCA before I ever laid eyes on the truck and have already gotten paid by FCA. He said the only option I have is to let them try to de-mold the truck and repair any leaks and accept that truck.
Don't know where you're located but things must be REALLY different in your neck of the woods.....I've never heard of any car dealership let anyone drive off the lot with a vehicle (other than a test ride when they are with you) and/or say "go ahead and drive it away" via telephone without having a signed agreement/contract, odometer disclosure form (federal law that one must be certified upon purchase and before vehicle is released to buyer and HAS to be signed - how did they get around that??), Lemon Law forms, declining of extended warranties, GAP, etc. What was the expectation??? That you'd return at some later time and square this all away? Who supplied the temp. registration? ...and if you're in a state that requires insurance (and pretty much every state does but New Hampshire & VA), you'd never be able to get the keys for said veh. until you had an insurance binder faxed or emailed to the dealership before you'd be allowed to leave...especially for a financed vehicle.
If they failed to do most or any of this as you say, then you really have them over a barrel.....not only if they didn't lock you in with a signed agreement but you can report them for failing to properly divulge and record the odometer cert. ,etc.