I do not really recognize a scenario that might lead to a solution, but is there any chance some of your media files might be corrupted? Maybe media center is trying to open a file in a library and encountering problems. I think I remember seeing some folks having problems if a folder or files was linked inside a library to another folder.
For media player, are you running a homegroup, or do you mean on one computer? Are the other users Admin users on the same computer? Perhaps some sharing or sync settings could be adjusted.
Sorry I can't read many of your attachments.