It's supposed to be done. Doesn't mean anyone really cares. You can imagine how many people actually bother to do it. I've even heard of some going to police stations being told to go away since it was wasting their time. I don't expect they really care unless someone feels like "setting an example".
http://lawandborder.com/temporary-residence-registration-for-foreign-nationals/
Q1: What does the Exit-Entry Administration Law require?
“Article 39. Where foreigners stay in hotels in China, the hotels shall register their accommodation (住宿登记) in accordance with the regulations on the public security administration of the hotel industry, and submit foreigners’ accommodation registration information to the public security organs in the places where the hotels are located.”
“For foreigners who reside or stay in dwelling places (住所) other than hotels, they or the persons who accommodate them shall, within 24 hours after the foreigners’ arrival (入住) at that dwelling place, go through the registration formalities with the public security organs in the places of residence….”
Q2: What are the penalties for failure to register?
“Article 76. Under any of the following circumstances, a warning shall be given, and a fine of not more than RMB 2,000 yuan may also be imposed: ….”
“(6) Persons concerned fail to go through registration formalities in accordance with the provisions in the second paragraph of Article 39 of this Law.”
I've gone through some strange things too, such as taking a taxi outside the boundary of a city. I guess the important thing to understand that there isn't strictly freedom of movement in China. They had some sort of border inspection where we were asked to produce ID. We pulled out our US passports, and the inspector looked at them and yelled out something - I was told in line with "What am I supposed to do with a US passport?"