Unfortunately, I can't easily share maps, as publishing outside the organization is controlled by a central administrator. I can, however, describe how I created it.
I exported several polygons and one set of points as shapefiles from ArcGIS 10.0 Sp4.
I zipped the shapefiles.
I added the polygons directly into the map.
I added 2 blank "editable" layers directly into the map.
Adding the points directly into the map didn't work, so I added them to "my content," and created a feature service.
I changed the settings of the feature service so that editors can "add, edit, or delete" features.
I added the feature service to the map, and ensured it was listed as editable.
This resulted in a map that can be viewed on collector, and the points are editable. I confirmed that changes made on the device are reflected in the arcgisonline map (and visa versa) However, as I mentioned before, when I attempt to add a new point using collector on Android, I get the error message "no collectable layers are visible." I have tried changing the "sync" settings to no avail (although I didn't really expect that to matter).
I hope this helps you help me!