Some have suggested that to get spaces at the end of a line to underline (using the "U" button in the editor), they need to add a period or something at the end of the spaces; otherwise, the spaces get ignored for underlining. While this is true (seems like it should be an easy fix, Autodesk!), some also said that they don't like the look of the period at the end, which of course, looks bad. A good workaround is to go ahead and use the period (or any character), then select JUST THAT CHARACTER and set its color to background (255).
This only works for paper space plots, it will still show up if you plot from model space, but at least it's a working kludge...