upgrading I do like this:
get the latest WordPress.zip
extract on my PC
Make a BACKUP of my database!!
using ftp (filezilla) I rename on the (running) site the folders
wp-admin to wp-admin-old
wp-includes to wp-includes-old
copy the new wp-includes and wp-admin up to the server and replace (just overwrite) the root files coming with the WordPress package. (wp-xxx.php index.php xmlrpc.php)
leave config.php untouched!
leave other files you might have there like .htaccess, robots.txt, sitemap.xxx also untouched
the folder wp-content stays as it is!
you might put the new akismet plugin and the new theme 'twentyten' in the place they should be.
after that, login to your admin, it will say the database has to be upgraded.
Do this and come to the dashboard, almost the same and smooth running.
now you can delete wp-admin-old and wp-includes-old on the server.
I got more than 10 sites, never problems upgrading like this.
Check the error.log after a while to see if any (old) theme function creates errors other than before, normally not!