This may happen to you in that web pages for anonymous users (i.e. not logged on) stay stale even when you use “Delete Cache” in WordPress dashboard and clear the data from your browser. The page contents stay stale and menus (if they were changed) stay on the old layout.
If this happens to you and you are pulling your hair out in testing and unable to get the pages to display on the new content then ssh into your server and check the permissions (ownership) of the /wp-content/cache is actually owned by the web server and has not been changed..
After a Plesk/Parallels upgrade (automatic I think) the user that Apache ran in changed and this meant that files that were previously created by Apache using the old user account were now not able to be deleted by the new Apache account user (www-data). This is probably never going to be seen on shared hosting but could be seen on virtual or dedicated servers.
The WordPress site would have kept dishing out the old file not matter what I did because the old cache files couldn’t be deleted.
The fix is easy (assuming your Apache installation is going to remain stable) and that is to ssh shell into your account and delete using the file owner (or root) the contents of the /wp-content/cache directory (which will have a “meta” and supercache” subdirectories.
You may also be able to use your FTP client to do the same but probably the cache directory won’t actually be visible at all.
Once you have deleted all of that old stuff then go back into the wp-super-cache plugin settings and remove and then re-enable the cache settings.
Non-logged on browsers will now correctly display the site and the supercache/www.example.com/… files correctly build up with the ownership being the Apache web server.
To test this I use Firefox and Opera: Firefox is logged in and Opera is used to display the web site as an anonymous user. Opera has a nice feature in Opera -> Settings -> Delete private data that you can quickly clear the browser cache of everything.