A very helpful person at the ThingWorx helpdesk investigated this issue for me, and determined that the wording in the Menu Widget help documentation was misleading. You cannot pass a parameter to a service from a menu widget. Instead, I am going to use a data-driven repeater widget to handle my menu options.
Please note that it can actually be done by using Session Parameters.
Not that I encourage the use of these, but if you have Session based values that need to be used in unrelated mashups, Session parameters is the way to go.
if however there is a relation between the mashups, usually this means a drill down of some type, I would recommend using the Navigation widget.
Either as a clickable button or a double click triggered service.