If I move or delete a file which has multiple parent collections, it will be moved or deleted from all those previous parents. This is totally an unsafe operation because:
There is no way to distinguish between multi-parent and single-parent objects from within the browse page, so someone may unexpectedly move or delete files which are also referenced by other collections.
As a suggestion, those multi-parent objects should be easily distinguishable from normal ones.
For example you can put an icon behind those multi-parent objects for two reasons
1- they can be simply differentiated by eye
2- putting the mouse pointer over the icon, pops up a list of parent collections