Those objects are stored into .Shared files that are always along the original QVW in the User Folders. Try stopping the QlikView services, backing up the .Shared file and renaming it, then restarting services. Test if you can add a new object and then delete it.
Make sure users have permissions to write or modify in the folder if the server is set to NTLM/NTFS
Yes, if you rename the file it will affect all users because all store the info in the same .Shared file. It seems more a corruption of the file or something.
Take a look at the file with the QlikView Power Tools in http://community.qlik.com/docs/DOC-3059 in perticular the Server Object Handler, and see if you can change ownership to an admin user and then delete the object.