Strange problem with upgrading wp on 2 servers

I have a website which runs from 2 servers (which share traffic). The blog is served from both servers while database is maintained on the 1st one only.
Let server 1 be the one hosting database.
Let server 2 be the one querying server 1 for database. (it has ip address of server 1 in the wp-config file instead of localhost).

Today I upgraded from wp 2.0.4 to latest wp 2.3.3.
I completed the procedure for server 2 first. After upgrading, I saw the error 2.3 database errors / wp_post2cat does not exist coming on my blog on server 2.

Ignoring this error, I upgraded WP on server 1 now. Something strange happened. When I clicked on my site.com/wordpress/wp-admin/upgrade.php it said that my wordpress is already up-to-date. I had not even clicked the upgrade button. Just uploaded the files, and i got this notice. And strangely, the 2.3 database errors / wp_post2cat does not exist went away. I am not sure if the wordpress on server 1 has been upgraded properly.

Can someone guide about what exactly happened? Do i need to do anything more?