My iMac (2011) wont shut down properly!!

Question

I have contacted apple's phone support 3 times but it still won't shut down properly.
1. they asked me to do a pram reset
2. they asked me to go into the safe boot mode (and it does shut down properly)
3. they asked me to clear my cache (it shuts down after i cleared it but i have to force shut my computer and wait until i swicth it on again to empty the bin and then it shuts down properly)
4. they asked me to reinstall my OS(but thats such a hassle and there shldnt be a problem with the OS bcos it shuts down normally on safe boot)
Are there any other solutions to this? It's been happening for the past 3 months... I suspect that it's the third party applications that are causing these problems. I tried reinstalling them but it still won't shut down. (eg, photoshop, filezila, firefox)
HELLP!!

Answer 1

If you're able to boot, launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ If you’re running Mac OS X 10.7 or later, open LaunchPad. Click Utilities, then Console in the page that opens.
Select the most recent panic log under System Diagnostic Reports. Post the contents — the text, please, not a screenshot. In the interest of privacy, I suggest you edit out the “Anonymous UUID,” a long string of letters, numbers, and dashes in the header and body of the report, if it’s present (it may not be.) Please don't post "shutdownStall" or "hang" reports.
If you can't boot in the usual way, try a safe boot. The instructions provided by Apple are as follows:
Be sure your Mac is shut down.
Press the power button.
Immediately after you hear the startup tone, hold the Shift key. The Shift key should be held as soon as possible after the startup tone, but not before the tone.
Release the Shift key when you see the gray Apple icon and the progress indicator (looks like a spinning gear).
During startup, you’ll see a progress bar, and then the login screen, which appears even if you normally log in automatically. You must know your login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.
Safe mode is slower than normal, and some things won’t work at all.
Note: If FileVault is enabled under Mac OS X 10.7 or later, you can’t boot in safe mode.