If you are on a version of Access before AC2007: Search this forum for "Securing a Database" and "Workgroup Security." I suspect that what has happened is that your users have the default SYSTEM.MDW because the database hasn't been properly secured. In such databases, every user comes in as SYSTEM, which by default has the permission to do an OpenExclusive on the database.
If you secure the database properly, you could restrict your non-adminstrator users to have only OpenShared permission on the database object, and that would solve much of your problem right there.
If you are on Ac2007, I must defer to others. Haven't played with that version yet.