Mountain Lion took a long time to install. I had negative time remaining at one point with the progress bar full, then it jumped back to being half full and showed I had 19 minutes left...for about half an hour. Total install time was nearly three hours. Of course now that it's all installed, it doesn't matter, but I was worried for awhile.
Safari 6 slows to an absolute, constantly-beachballing crawl if I have around 20 tabs open. Responding to a right click in a web page, or responding to a Command-W or x-ing out a tab may take as long as 10 minutes. Not even close to kidding. I pressed the 'x' on a tab, got up, washed a few dishes, made some tea, sat back down, had a few sips, and then finally the tab closed. During this time (and when this happens in general), the cursor became a beachball when moved into web content, and while I could switch tabs, I couldn't interact with any page in any tab in any way. Right-clicking the Safari icon in the Dock didn't give me the option to Force Quit, so ML must have thought everything was just fine. Command-Q does quit Safari immediately when it behaves this way.
Also have problems with Safari using massive amounts of CPU somewhat randomly. With a few tabs open with pages from this forum, CPU utilization will sometimes suddenly shoot up to 160-200% and sit there until I close most tabs. Any presence of Flash on a page whatsoever will immediately bury the CPU at 200% and keep it there, rendering the whole machine sluggish and murderously hot. Safari 6 under Lion didn't seem to do this, though I only used it for a few hours, so who knows.
Two-finger swipe from the right edge to bring out Notifications frequently doesn't register. I have to be super careful. It's really not that troublesome, but I hope Apple tweaks it a little in future point releases.
So other than one very temporary annoyance during installation and a mildly annoying gesture issue, the only real problem is Safari 6. Overall, though, ML runs ever so much better than Lion. With Lion, I routinely had strange glitches and various issues that really grated. There wasn't a time when I used my machine that I didn't wish I was back on Snow Leopard (whose install disc I wasn't able to find or I'd have gone back fast). So far with ML, I'm really, really pleased. I haven't once had the urge to dive into my storage shed to locate my Snow Leopard disc. I'd call that an improvement.