Just as in Germany or Denmark you are legally bound to register for residence in China as well. This has to be done within the first 24hrs of your arrival. Police inspections are not unusual and if you are found without a police registration you will have to accompany the police to the station and pay a fine (up to RMB 500 per day!)
If you aren’t registered correctly by the time of inspection, sanctions imposed by the police might well be the consequence. The landlord will accompany you to the police station and either help you with the registration or even do it all for you, so it shouldn’t be a problem really.