If you are expecting a lengthy post with detailed list of encountered problems and their solutions, you will be disappointed, because... there were none.
We just clicked the Upgrade button in Update Manager and left the computer for a few hours to download the updates. Then, after the installation began, we answered 3 or 4 questions whether to keep or replace some configuration files (we replaced them all, but kept the copies of modified files just in case) and that's it.
After restart we had a laptop running Ubuntu 7.04 and everything - wireless networking (with WPA), sound, graphics - was working properly. No problem at all.