I also experienced lockups (spinning beachball) and noticed this happening when I was at conference last week and disconnected from the internet. This was a bit freaky as I was presenting and needed my mac and my slides to run smoothly. I booted my machine 30 minutes before my presentation and had little time to work through mac issues.
I experimented a bit afterwards and noticed that the issue would reappear when working "off the grid" and disappear after the mac was re-connected through wifi. Since I was not trying to access the internet, I have no clue of the cause of the problems. Seems like the mac was hanging while trying to access a remote server.
I never had such issues before upgrading to ML and I have not changed anything on my Mac since the upgrade. But the huge issue for me is the Mountain Lion Sleep issue. This is well documented already. Basically, I have to leave my mac awake all the time as it will disconnect my network drives after sleep. This unables all my night backups.
I would go back to Lion without hesitation if I had a good way to do it. Good lessons learned, I will clone my machine before any Apple OS update in the future.
If you are reading this and wondering whether to upgrade to Mountain Lion. Please make sure you read all the OS Issues before making your decision. To me, 10.8.2 is still a buggy beta version with serious show stoppers. It should have never been released by Apple in this form.