When you choose to order by menu_order and then use the pagination WP action, it does not work because the second page gets a random order for any menu items that are the same order number as another order number. Often when using menu_order many of the items will be left as the default of 0 and since PG does not allow for a secondary order by value the rest of the posts get queried as a random order and posts on page 2 are likely to show up on page 3 because WP does not know how to handle posts that have the same order_number when the loop runs again for the next page.
This bug can be worked around if one adds the second order by parameter (for example date or title) manually to the loop args.
I quick permanent fix for this bug would be to allow the user to select multiple order by from the current dropdown. Right now only one can be selected.
In general it would be nice if the UI for WP loop actions allowed users to access all possible parameters.