When you get back and are fully re-registered, ask for a copy of the forms you fill out at the local cop shop. That will make life a little less exciting. Do note that there are multiple levels of police, so you may still get visited. My res permit involved visits to 4 different police stations.
Yes, the hotel is generally supposed to do it. It's a simple form you fill out when you register. They should take that and a copy of the passport to the police for you. I try to be a law abiding resident, but have forgotten about this a couple times when the hotel didn't shove a form in my face. So far, I haven't been locked up for it (yet).
One of the hotels in Yunnan my fiancee tried to book reservations at rejected the reservation since they weren't permitted to have foreigners (or weren't competent enough to do the paperwork).
The real fun is going somewhere during any of the big holiday periods. The police are still in business, but the desks where silly things like foreigner registrations are handled are often closed.
Just to make my life more entertaining, I need to renew a whole bunch of papers and permits in March, including my residence permit. If there is any delay, I'll be out of the country for my wedding.