All the 'errors' above are actually Notices and Warnings - so they aren't necessarily show stoppers.
The debugger in wp_config probably increases PHP's error_reporting level which accounts for the increase in Notices and Warnings.
However, strictly speaking, some of these Notices should really be dealt with - they are indicating a potential vunerability in the code. eg.
Notice: Undefined variable: page_title in D:\phpsites\buzzz2\wp-content\themes\thesis_18\lib\classes\head.php on line 41
This is saying that $page_title is being used in some context without it first being defined or initialised to something. This is just bad programming practise. PHP will probably default this to NULL, which casts to an empty string in a string context - so if that is OK, then it still works
Warning: Cannot modify header information - headers already sent by (output started at D:\phpsites\buzzz2\wp-includes\class-http.php:1045) in D:\phpsites\buzzz2\wp-content\themes\thesis_18\lib\functions\compatibility.php on line 7
This is due to the Warnings/Notices output previously, so as long as there are no other 'errors' then this is OK. HTTP Response Headers (eg. Cookies) cannot be sent (again) once page content (in this case the error messages themselves) are already sent.
Notice: register_sidebar_widget is deprecated since version 2.8! Use wp_register_sidebar_widget() instead. in D:\phpsites\buzzz2\wp-includes\functions.php on line 3237
Wordpress specific Notice. Ok for now, but might break completely in future versions of Wordpress when the method is removed.
Warning: fopen(http://www.buzzz.org.uk/buzzz2/wp-cron.php?doing_wp_cron) [function.fopen]: failed to open stream: HTTP request failed! in D:\phpsites\buzzz2\wp-includes\class-http.php on line 1045
I'm not sure whether this is because the resource (http://www.buzzz.org.uk/buzzz2/wp-cron.php?doing_wp_cron) simply could not be found, or because the HTTP (protocol) wrapper is not enabled in your installation of PHP (controlled by allow_url_fopen setting in php.ini).