Just did the update for 10.10.2. Worryingly all I got on restart was a black screen! So, after trying various things I pressed the power button down for ten seconds until I heard the machine switch off. The power button again to restart.
Still a black screen.
Then I realised that it was the login screen (it wouldn't cmd-tab) so I put in my password and I could tell (again cmd-tab) that it had booted up. Still a black screen.
Closed the lid, ten seconds later opened it up again. Still a black screen.
Getting rather p'd off with Apple / Yosemite. Windows 8 would be an improvement at this point. It's a $3,000 paperweight.
Thinking this is a visit to the Genus bar and let off both barrels at Apple (they deserve no less for Yosemite and the problems it's caused) decided to try one last time.
Closed the lid and waited a minute before re-openning it. Finally something worked! I could tell the graphics of some windows were screwed up as it hastily cleared them.
I'm now frightened to close the lid again.