First make sure you have removed any duplicates from your library before you begin to cite references in your Word document. This is important to avoid any errors in your bibliography.
If you are workig on a shared document with a group of colleagues, each member of the group must have the references you are citing available in their own Mendeley Desktop library.
One way to ensure all of your collaborators have access to the same references is to create a Mendeley group.
When you insert citations into your Word document, you can choose to search references in a particular group by selecting that group from the drop-down menu, instead of My Library. Citations you insert will then be selected from those in the group.