Is it safe for me to update to 3.3?

read the troubleshooting 3.3 master list: https://www.ads-software.com/support/topic/troubleshooting-wordpress-33-master-list

Make a backup of your files and database first:
https://codex.www.ads-software.com/WordPress_Backups
https://codex.www.ads-software.com/Backing_Up_Your_Database

See if your host has the minimum requirements for running WordPress 3.3:
https://www.ads-software.com/about/requirements/

Disable all plugins before upgrading. I would upgrade in steps: 2.3.1 to 3.0 to 3.3 (or even smaller steps) and make a database backup after every step:
https://www.ads-software.com/download/release-archive/

https://codex.www.ads-software.com/Updating_WordPress#Manual_Update

DONT upgrade whatever you do. Some elements of my plugins have stopped working. And no way to backgrade.

@spinlessplates
You make a backup of the database before upgrading so that you can always backgrade to an earlier version if needs be. I’ve got lots of 3.3 sites working perfectly well.