Since my previous post I have restored the system to the point where all the updates were installed, and I've run qfecheck to check that they are installed properly. I have checked that the settings in User Rights Assignment are identical to the ones in my screenshot.
To check that I didn't miss something before, I tried again adding a new user and adding them to the Power User group, but with the same result as previously. They show as a member if I look in Computer Management > System Tools > Local Users and Groups > Groups > Power Users, but if I look in User Accounts they show as "unknown account type". If I change it to a "Limited" account it retains this setting - until I add it to Power Users when it becomes "unknown" again.
Just a thought: are the updates for XP Pro normally the same as for XP Home? The updates list from WUD did not specify which version, but they all installed OK.