On a shared desktop PC running Ubuntu 12.10, there are multiple users with full administrator rights. Can one administrator see the content of other administrator's account?
Yes, by default config every user can see every home. You can change this setting, if you want. See this guide on help.ubuntu.com
As Eliah Kagan noticed, administrators will still always be able to use their administrative powers to see into anything inside any user's home folder. If you want to avoid that, you have to encrypt your home.