First of all, we are working hard on refactoring the client, writing API docs and making it easier to build new widgets. We'll have new widget tutorials up for the 3.0 release as well.
A good example from the AppStore really depends on what sort of widgets you want to build. If you want to use reference sets, the Checkbox Set Selector is a good start. For an input/attribute widget, try the Prefilled Inputbox.
The code for our own internal widgets is not open-source. It's no big secret but it isn't made to be easily readable and has a lot of hooks into our internal libraries. I don't think this would help you very much. I suggest you look at all the widgets on the AppStore, these should cover any situation in a widget concerning the Mendix API.
A good grasp of the dojo library is not neccessary, but it does help. Dojo provides a lot of shortcuts and convenience functions you can implement. Do note that we run Dojo 1.3, so newer functions might not be available. You can easily inspect this using Firebug in a Mendix application and opening the dojo object on the window.