I've noticed some strange behavior with the standard Measurement widget, I wonder if others have noticed at least some of these things and they might get addressed.
Clicking the 'Clear' button while you have an active measurement (before you double-click to finish) causes some buggy behavior when you start another measurement. It will include the final point of your previous measurement, and if you double-click to finish, it will draw all of the geometry from the previous measurement, though it does not include those distances in the measurement total. Also while this is happening, the measurement totals are not dynamically updating as you move your cursor.
I think it should be fixed by either making the 'Clear' button do nothing until you have double-clicked to finish your measurement, or have the Clear button delete any remnant of the previous measurement. It also wouldn't hurt to have some indication (a tooltip or message on the widget window) that you should double-click to finish your measurement, since this is not always obvious to less GIS-savvy users.
The other main issue is that there are some actions that cause the measurement geometry to become clipped and invisible while you are actively measuring. The easiest way to see it in action is to start a measurement and continuously pan the map as you are measuring. Sometimes continuing to click your measurements (or finishing) will cause the geometry to appear, sometimes not. It seems like other actions will trigger this behavior but I haven't been able to isolate them. I've noticed this in other widgets that use draw tools. It appears to be an issue with more recent versions of the JSAPI, I can load up an old v2.1 WAB app and can't duplicate the problem.