Yes.  The primary issue I've encountered is with geoprocessing service widgets.  Since the size of the frame holding the widgets is designed for desktop, when viewed in a mobile device the frame often takes up the entire screen.  If you just need to enter some value and then execute, this is not a problem as you can close the widget frame after executing.  But if you want to, for instance, make a path by interactively placing points on a map you have no map real estate to work with.  This is a problem, as far as I can know, only with widgets that require interacting directly with the map, i.e. creating a feature set before executing the widget.