I too use the right-click button as an instructional tool. In working with this option, I've never seen a menu not show up. However, I've had two situations occur: 1) the first time the menus are loaded, there can be a delay. On some computers, it can be noticable. 2) sometimes one can click on a phrase, either the input or output, and there is nothing for which it can do to it.
From a pedagogical perspective, I teach the students to write some simple code. For me, nearly all of the math problems can be performed upon learning about 10 commands. But I use the right click for maybe that calculate that requires at most a couple clicks. For a different pedagogical perspective, Robert Lopez should weigh in here.