Generally speaking, if you are receiving certificate errors, it means the website(s) you are visiting are having certificate problems and it does not indicate a problem with Internet Explorer. And there's really no way to turn off or disable the warnings. About certificate errors
You could try manually deleting untrusted sites (those sites that are generating the certificate warnings) and if the site has updated its certificate you may no longer get a warning for that specific site.
In the Start Menu search box, type in "certmgr.msc" (without the quotes.) Wait for a list to generate. Click on "Untrusted Certificates" (left column) and double-click on "Certificates" (right column.) Highlight each certificate you wish to remove, right-click on each certificate then select "Delete." A pop-up will appear to confirm that you really want to delete. Press "Yes" when prompted. You can also access your security certificates in Internet Explorer by opening Control Panel > Internet Options > Content tab > Certificates button > Untrusted Publishers tab. (You may have to use the small left/right arrows to scroll to the Untrusted Publishers tab.) Highlight and delete each certificate that you wish to remove.
Couple more things you can do just for general maintenance. Upgrade to IE9 for better overall security; run a system file checker scan to make sure you don't have any damaged or corrupt system files; run disk cleanup to remove temp files that could be returning you to a corrupt/damaged website.