I have updated WordPress again to version 2.6.1. This time I used a plugin called Automatic WordPress Upgrade. It worked amazingly well. It first backed up my files then my database, which it let me download. Then it automatically downloaded the latest version of WordPress from the wordpress site, put the site into maintenance mode then de-activated all the plugins. Upgraded the WordPress files, re-activated the plugins and cleaned up after itself. It was a very smooth and painless process.