This is not really an "upgrade problem", but it is the best fit as far as I can tell.
I moved a site I developed on a site using mysql 4.1 to a server using mysql 4.0. I used the 4.0 compatibility flag as suggested here (and in other places) when exporting.
The site looks fine and navigates fine, however, when I go to log in, I get the following errors:
Warning: Duplicate entry '0' for key 1 query: INSERT INTO watchdog (uid, type, message, severity, link, location, referer, hostname, timestamp) VALUES (1, 'php', 'Duplicate entry '0' for key 1\nquery: INSERT INTO watchdog (uid, type, message, severity, link, location, referer, hostname, timestamp) VALUES (1, 'user', 'Session opened for <em>Webmaster</em>.', 0, '', 'http://wisdomword.com/user', 'http://wisdomword.com/user', '64.4.106.234', 1157693073) in /home/wisdom/public_html/includes/database.mysql.inc on line 120.', 2, '', 'http://wisdomword.com/user', 'http://wisdomword.com/user', '64.4.106.234', 1157693073) in /home/wisdom/public_html/includes/database.mysql.inc on line 120
Warning: Duplicate entry '0' for key 1 query: INSERT INTO watchdog (uid, type, message, severity, link, location, referer, hostname, timestamp) VALUES (1, 'php', 'session_regenerate_id(): Cannot send session cookie - headers already sent by (output started at /home/wisdom/public_html/includes/database.mysql.inc:120) in /home/wisdom/public_html/modules/user.module on line 943.', 2, '', 'http://wisdomword.com/user', 'http://wisdomword.com/user', '64.4.106.234', 1157693073) in /home/wisdom/public_html/includes/database.mysql.inc on line 120