There are some differences between normal widgets and mobile widgets you should be aware of. In short:
In order to be able to use a widget on a mobile form, a widget should be defined as being a mobile widget in the xml definition:
<widget id="custom.widget.HelloMobileWorld" mobile="true">
Mobile widgets are declared using dojo.declare instead of mxui.widget.declare, and should inherit from mobile.widget._Widget. For an example, see the mobile widget lifecycle documentation.
The mobile user interface is defined in its own namespace: mobile. Everything defined in the mxui namespace is not available on mobile. Furthermore the 'mobile client' uses a different user interface subsystem (mx.ui) which defines a different API in mobile.
Although mxui.widget.Widget and mobile.widget.Widget do have a lot in common, there are some differences (see the documentation for details).
P.S. Mendix 4.0 uses version 1.6.1 of the Dojo Toolkit.