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Check wp-config.php for any lines that define a $wp-> object setting.

They will break wordpress 3.1 or higher and give a $wp->add_query_var error.

For example:

$wp->cookiedomain = '.example.com';

Will work in 3.0 and below but break WP 3.1 and 3.2

You’ll have to research for the replacement define setting as an alternative to $wp->

For example, the modern replacement for the above line is

define(COOKIE_DOMAIN,'.example.com');