System Information
OSX iMac 5k

Blender Version
2.78b

Short description of error
You need to do a 'physical' object mode toggle instead of programming that toggle to do mesh operations on python selected faces/edges/polys

Exact steps for others to reproduce the error

-Add a cube
-Enter this in console:

obj=C.object
pols=obj.data.polygons
bpy.ops.object.mode_set(mode = 'EDIT') 
bpy.ops.mesh.select_all(action = 'DESELECT')
bpy.ops.object.mode_set(mode = 'OBJECT') 
pols[0].select=True
bpy.ops.object.mode_set(mode = 'EDIT') 
bpy.ops.object.mode_set(mode = 'OBJECT') 
pols[1].select=True
bpy.ops.object.mode_set(mode = 'EDIT')

press I (for inset)
Should work as expected
press F6 to tweak

Observe Erratic behaviour: Nothing gets updated!

Observation: before pressing I, toggle Object/Edit mode by hand (TAB) and then use Inset will work
Toggling by python instead of by hand won't make it work..

I've noticed this problem when working on a script which does the following:
Enter Edit mode, and as an example set Face Selection Mode.
Select faces
Put those selected faces.indices in a buffer
Select other faces
Do a boolean operation on those two selections
Works as expected..
However, with those selected faces, trying a mesh operation like inset or bevel will work at first, but when pressing F6 afterwards, Blender will instantly revert back to it's last 'official' selection..
A little bit different in result, but similar.. hope this is the same bug.
The script needs to toggle back and forth between EDIT/OBJECT mode, thus creating a similar situation as in the bug report..
To prevent F6 from failing, I have to toggle MANUALLY between EDIT/OBJECT mode to get it to accept the complete selection. Python toggling the mode won't help..

Hope it all makes sense,
Regards,
Roel