I have a model where I would like to rotate an area of the object, in this case a mouth of a ordinary beast along a defined point, marked here with the 3D Cursor. And I am trying to move the selected areas Origin Point to the cursor, so in edit mode i press Ctrl+Shift+Alt+C and select "Origin to 3D Cursor. But then I get an error message that says, "Operation cannot be preformed in edit mode". Why??
What I understood about your issue, you want to open mouth and close it.
Please try following steps:
You may also create a Shape key for easy rotate and animate
When you are done with it you may change back the Pivot point to Median point
Best of luck!