Mac won't start automatically after Mountain Lion update

Today I found the latest Mountain Lion update in the App Store and I started the installation. It seemed to be working fine so I left the room for a while to do something else while it was installing. However, when I got back, Mountain Lion hadn't started by itself, and I was left with nothing but the "grey background" (if you know what I mean) that shows up during the installation.

Nothing happened so after a while I had not choice but to reboot the Mac myself by holding in the on/off button at the back. I'm not an experienced Mac user so I'm a bit worried. Does this happen often and does it mean something could be wrong with my iMac?

After the reboot I entered the App Store again to see if the update was still there, but it wasn't, so I guess the installation itself went well. I just got a bit worried that something's wrong with my iMac. I just bought it.

Thanks for your help! 🙂