> specifics of what can happen?
Lots. Body damage, tire damage (from the clamps), steering damage (from
thrashing), hand brake, transmission (less likely on a standard), lost
items (they forget to lock it), and then the worst thing is finding
something wrong and wondering if they did it or you just didn't notice it
before.
And thinking about it, I can remember a few other things, like if you have a rear wheel drive, some towers will just assume that you have a front wheel drive because it's more common and cause damage that way. Since I have a fairly standard car, that's less worrisome.