Is there a way to add bulk operation options to the admin/content list's 'Update Options'? I have downloaded the views bulk operations module and activated it.  I offers me many new options for changing the settings on my nodes/entities.  I would like to know if there is a way to add these options to the "update options" which is available on the content page of Drupal admin (location: admin/content.)

This menu already lets you do things such as publish, unpublish and delete.  It also picks up options from add-on modules.  It seems that views bulk operations should appear in this menu too.
Bulk operations provided by that module only make sense in the context of a view, so you won't see them on a non-view page like the standard admin content page.

You can install the Administration Views module to replace that page with a View, and then you should see the options you're expecting. Most (all?), of the core actions from the original page should be available. To add more, you can edit the View and change the available actions in the VBO field.