Looks like selection by mouse is not possible. Pressing F4 will bring up the Property window. There is a listbox at the top that will list all of the objects in the report, so it is possible to select one, then use the arrow keys to quickly cycle through all the objects (looking for the handlebars in designer to know you have the correct object). This is the closest I can get to a solution.
That interface is "almost" like the Report Explorer in CR Designer except all the objects have no hierarchy data.