Last question first... if the registration stickers on your BMW are expired, yes you may get stopped and cited; even at times by a parking officer. You can visit a local DMV office and purchase a 30 day temporary tag for $50.00.
In terms of the smog check failure it appears your BMW is having trouble setting or completing the required Emission Monitors. Monitors are internal self-tests which the Engine Control Unit performs to ensure the computer system is functioning properly.
The link below is a .pdf of the Federal Test Procedure (FTP) Drive Cycle used by BMW. Following the drive cycle procedure properly (and assuming your BMW has no existing emission problems) your BMW's emission monitors should complete.
FTP Drive Cycle For BMW