There are a lot of people bemoaning the 'fact' that they can't get a residency appointment, but as far as I'm aware none of them have yet reported what happened when they asked at the actual police station. That's the sort of input that people need.
I know of one police station in Valencia province where they are still processing them, and doing so very nicely thank you. Apparently it's possible to lodge all your application paperwork with them, wait for confirmation that everything is acceptable, and then just go along in person to prove your ID.