Q: security update 2016-001 hangs

I had the same problem. I rebooted and it was a normal start. I went to the  menu with the option/alt key held down and ran System Information. The update had not installed. I downloaded it from the link below and successfully installed it.

Security Update 2016-001

You are welcome.

I have this question also.  It worked on my Mid 2010 Mac Pro but sat there so long I thought it was frozen.  Also no problems on my MacBook pro late 2008.  However, when I tried to install it on my wife's late 2009 Mac Mini it refused to download the entire file.  It downloaded approximately 150MB, and then completely stopped downloading.  I tried several times, and at each time it stopped at a different amount of data. 

EDIT:  I was able to download the complete file from the link above and it installed correctly.  Problem solved, but it would be interesting to know why it was unable to download correctly from software update.