Download older Version of Mountain Lion from App Store

...is a way to download an older Version of Mountain Lion from the App Store?

Nope, your stuck with it breaking things or being buggy, no way to revert to a earlier verison.

If you made a bootable clone you could, simply hold the option key and boot off the clone and reverse clone 10.8.4 back on.

Most commonly used backup methods

So since you can't go back, you can attempt to fix in place, provided it's not a OS X bug that has to be fixed.

..Step by Step to fix your Mac

Your likely going to need to do #8 and restore OS X over itself, any third party software that doesn't work, check for a update or problems on the developers forums BEFORE reinstalling it or your problems will most likely return.

If you have Mountain Lion on an install disc you can install again and then update with the Mountain Lion Combo update. Download from here http://support.apple.com/kb/dl1659

What exact version of OS did the machine come with?

If you have a backup, there is one way you could try, but that will wipe out everything on your hard drive: boot into internet recovery (hold Command + Option + R during restart), and once connected to Apple's servers, go to Disk Utility to wipe and format your drive. It will then automatically download/install the original version the machine came with - IF that was lion or Mountain Lion. You can then update if desired.

If it was Snow Leopard or earlier, then you'll need to install disks.

If you have an install disc you dont' have to erase anything to install Mountain Lion from scratch. The documents and application on the computer will not be erased if installing on top what you have.

I don't think you can install an older OS on top of a newer one, which is probably why babowa is suggesting an erase.

Since Snow Leopard you can. Before that you couldn't. I must confess I haven't tried it with Mountain Lion but I have several times with Snow Leopard. Works fine.

Since Snow Leopard you can.

I've not heard of that; all the suggestions I've seen is that you cannot install Lion over Mountain Lion (as an example) unless you erase the disk first. In fact, I remember I had to do a reinstall while testing last year and had to wipe my disk first to get back to Lion. I do not know about Snow Leopard since I've not used it regularly for 2 years (I have a bootable partition with it and boot into it to use Appleworks occasionally).

And, in order to use Internet Recovery's ability to reinstall the original system, the drive needs to be wiped first. That has been tested.

If you want to import Mail data, you can try that, but you will need to drill down to the actual emails and import them into newly created folders as the folder hierarchy changed completely. I did this going from Snow Leopard to Mountain Lion and it took hours, but did work when I finally finished. Don't forget to rebuild each mailbox and then restart the computer.

As for addressbook: simply export all of your Vcards (as Export > Vcards) and copy the file from your desktop to the Snow Leopard desktop, then import them from there.

Can't help with iCal as I don't use it.

Have you tried booting into the Safe Mode? I didn't see that in the linked article. Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application uninstaller. For each disable/delete, you will need to restart if you don't do them all at once.

Safe Mode

Safe Mode - About

What's your definition of a "fresh" copy?

Regular recovery (Command + R) reinstalls the currently installed OS version on top of what you have.

Internet recovery (Command + Option + R) will reinstall the original OS version - IF that was Lion or Mountain Lion AND you erase the drive first. That would be a "fresh" install.

If yours came with Snow Leopard, internet recovery will not work. You need the install disks.