Back in February 2015, Tim Witt released a modified Coordinate widget that also shows current map scale. I took the scale-related elements of that widget and added them to the Esri Coordinate widget released with WAB Developer Edition 1.3.
Here's a screenshot of the widget working in an app made using WAB Dev 1.3:
To install, unzip and place "Coordinate" folder in the widget folder of your WAB Dev 1.3 app after deleting the stock Esri Coordinate widget:
I strongly recommend that you DO NOT replace the stock Esri Coordinate widget in the base widget folder (\WABdev_1.3\client\stemapp\widgets), as doing so will greatly complicate general app handling (e.g. duplicating, creating) and the importing of apps from WAB Dev 1.2.
Update April 1, 2016: Initial testing suggests that this widget works in WAB Dev 2.0.
Update July 19, 2016: Initial testing suggests that this widget works in WAB Dev 2.1.