You're right, mIRC isn't written wth modern multi-user OSes in mind. The reason for the issue is that by default it tries to save all settings into it's installation location (ie. c:\Program Files\mIRC) which will cause problems for users with restricted access. To get around the problem you can simply change your mIRC shortcut's "target" field to save all settings into a user-accessible directory by adding a command line switch like so:
"C:\Program Files\mIRC\mirc.exe" -r"C:\Documents and Settings\YourUserNameHere\My Documents\mIRC\"
(You'll have to create the directory first).
Of course this isn't an ideal solution but if you want to get mIRC running until this is fixed then it's the simplest way.
