Safari opens websites not using HTML formatting- Why?

Question

Can anyone help? This is what happens on many websites - such that I no longer use Safari : http://screencast.com/t/cmh3eNvkva
Safari gives me two problems:
1. Not formatting sites correctly making them unusable
2. Telling me that Site Certificates are untrusted (when they should be trusted - and are the correct sites)
I have tried everything I can think of - Clearing cashe - uninstalling and re-instaling Safari - upgrading Safari. Everything workd fine in Firefox - thank heaven.
But honestly, what's the point of a Browser - and a Mac one at that, which won't function properly?

Answer 1

Please read this whole message before doing anything. This procedure is a test, not a solution. Don’t be disappointed when you find that nothing has changed after you complete it. Step 1 The purpose of this step is to determine whether the problem is localized to your user account. Enable guest logins* and log in as Guest. For instructions, launch the System Preferences application, select Help from the menu bar, and enter “Set up guest users” (without the quotes) in the search box. Don't use the Safari-only “Guest User” login created by “Find My Mac.” While logged in as Guest, you won’t have access to any of your personal files or settings. Applications will behave as if you were running them for the first time. Don’t be alarmed by this; it’s normal. If you need any passwords or other personal data in order to complete the test, memorize, print, or write them down before you begin. Test while logged in as Guest. Same problem? After testing, log out of the guest account and, in your own account, disable it if you wish. Any files you created in the guest account will be deleted automatically when you log out of it. *Note: If you’ve activated “Find My Mac” or FileVault, then you can’t enable the Guest account. The “Guest User” login created by “Find My Mac” is not the same. Create a new account in which to test, and delete it, including its home folder, after testing. Step 2 The purpose of this step is to determine whether the problem is caused by third-party system modifications that load automatically at startup or login. Disconnect all wired peripherals except those needed for the test, and remove all aftermarket expansion cards. Boot in safe mode* and log in to the account with the problem. The instructions provided by Apple are as follows: 
Shut down your computer, wait 30 seconds, and then hold down the shift key while pressing the power button.
When you see the gray Apple logo, release the shift key.
If you are prompted to log in, type your password, and then hold down the shift key again as you click Log in.
Safe mode is much slower to boot and run than normal, and some things won’t work at all, including wireless networking on certain Macs.
The login screen appears even if you usually 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.
*Note: If FileVault is enabled, or if a firmware password is set, or if the boot volume is a software RAID, you can’t boot in safe mode.
Test while in safe mode. Same problem?
After testing, reboot as usual (i.e., not in safe mode) and verify that you still have the problem. Post the results of steps 1 and 2.