So Mountain Lion isn't perfect. It's got its flaws. But overall, it's a solid platform, and a lot of the smaller issues that pop up can be fixed with third party apps. Here's how to make everything just to your liking, using non-Apple software.
Clean Up the Notifications Gridlock
Notifications are terrific in Mountain Lion. But a lot of us have had that same functionality for a while now, with Growl. The problem? They don't play nice together; Notification and Growl banner alerts both show up in the same place by default. So, you've got a few options: Abandon Growl; move Growl's notifications to a different corner of your screen; don't use notifications and only use apps that have Growl support (Sparrow ($10), Adium, etc.); or use Hiss. You'll like that last option.
Hiss takes all of your Growl notifications, and converts them into Notifications. The big benefit is that all of your notifications will funnel through the same pipes. The bad news is that Notifications is way less customizable and full-featured than Growl. No click-through, no transparent banners, no multiple-banner alerts if a bunch come in at once. Plus, everything that's funneled from Growl displays as Growl notification, whether it's from Rdio or Sonos or Sparrow and Propane or whatever. Lame. But still an improvement.
A Smarter GateKeeper
GateKeeper is Apple's way of making sure you don't install anything dumb or malicious on your machine. It's just a little, shall we say, overzealous at times. On its medium-strictness setting, it makes it difficult to install well-known apps like Steam. Come on.
As an alternative, try deactivating GateKeeper and installing Little Snitch ($30, or free if you reenable every three hours) instead. It won't stop you from installing apps of unknown origin, but it does monitor every incoming and outgoing connection on your machine, and asks for confirmation before letting it go through.
This sounds like a pain, and it can be at first, but once your regular connections are all approved (forever), you have a much more manageable layer of security than GateKeeper. Or, you could just use the two in tandem.
Get AirPlay Mirroring Even if You Can't Get AirPlay Mirroring
You can only use AirPlay mirroring—one of the cooler new features in Mountain Lion—if you have a Mac made after 2011. That's when Intel's Quick Play feature was added to its Sandy Bridge processors. But don't feel left out! You've actually been able to mirror your computer's display to another screen for a while now, regardless of your Mac's age, using AirParrot ($10). AirParrot costs money, sure, but it gives you the same 1080p mirroring that freshly minted Macs have. It's worth it.
Fix Your Cowboy Rodeo Leather Skins
Yes, the BDSM/Rodeo makeovers to Calendar and Contacts are still ugly. MacNix is an easy solution. You just download two DMG files, run them, and magically, the skeumorphic leather skin is replaced with fresh, clean aluminium. It was even updated yesterday to look even cleaner in Mountain lion—the only remnant is a slightly brown font at the top of Calendar.
Actually Customize Your Gestures
Apple's never offered many customization options for gestures. You can fix that with BetterTouchTool, an app that lets you map literally any function to any gesture or keystroke. Want to launch Mission Control with a pinch? Done. Show desktop with two finger swipe left? Sure! Just be aware that there's such a thing as too much customization, where if someone else is using your computer they'll just punch you in the face instead of taking an hour to learn how to use two-finger scrolling.
Fix Messages' Crappy Log Search
So Messages is actually a really good desktop chat client. Thing is, it also sort of broke chat logs. They're still there, but the Search bar at the top of your messages window freezes the app for about a minute if you've got a lot of logs to sort through. And it's not very helpful after that, either. You can fix this one of two ways: Use Loghorrea to look through your iChat/Messages logs, or install Adium, which has always had the best archiving of the Mac chat clients.
The Better Browser
This might be obvious, but for all Safari's flourishes and improvements, it's still not the best browser on OS X. If you're not already, you should think about using Google's Chrome. Even if you're in love with all of Apple's additions to Safari, Chrome extensions can make up much of the ground. It's also got a lot of the same utility features, like cloud-stored bookmarks and tabs. Plus, its Shockwave Flash extension means you don't have to deal with full-on Flash, and the battery and performance issues associated with that. Just beware that Shockwave is giving a few of us, like Glorious Leader Joe Brown, some issues in Mountain Lion.
The Everything Fix
Lion Tweaks, and soon Mountain Tweaks, is the app for anyone with a lot of little complaints about Lion or Mountain lion. You can toggle a ton of the controversial tweaks on or off, like natural scrolling, or no key repeat, or resuming all your files when you restart an app. The Mountain Lion version isn't out just yet, but it's coming soon.