Actually I just determined that the problem IS Multi-Launch Box.

When MLB is running, Shift+Left Arrow and Shift+Right Arrow do not work on MLB as expected and they are both broken in all other applications - such as selecting one character of text at a time.

When I close MLB, I can use Shift+Left Arrow and Shift+Right arrow to select text again.

Does anyone know a good key broadcasting program for Mac? Besides the handful that are mentioned in the stickies on this site?