Mage_Catalog_Model_Resource_Category_Flat::isBuilt was introduced in CE 1.8 and does not exist in any versions prior. This means that either the core has not been fully upgraded, the site has an override in the local code pool or some old code is being cached in a byte-code cache like APC.
I would open
app/code/core/Mage/Catalog/Model/Resource/Category/Flat.php and look for the method there. If it is not there, you need to upgrade the core to match what is in 1.8.
Assuming the core pool checks out ok, take a look in
app/code/core/Mage to see if a file is there overriding the updated core class definition. If there is one here, it will take precedence. It would need to be removed and/or updated for 1.8.
If neither of the above are the issue, make sure compilation and caching are disabled in Magento, restart apache and/or php-fpm (if used) and see if the issue persists.