I have had a little more play and have taken a few more shots with better controlled conditions.
My impressions are based on the inspections of the JPEGS straight from the camera. These don't have any lens corrections to distortion, vignetting or aberrations because the camera does not know what lens is on - there are no electronic contacts.
F/2: Good centre sharpness, considerable falloff and corner softness. Contrast also relatively low.
f/2.8 Big improvement in contrast, falloff and corner softness. Centre sharpness also increases, but less noticeably.
f/4: Again noticeable improvement at the corners, although a smaller step than before. Small increase centre sharpness, no further improvement in contrast.
f/5.6: Peak centre sharpness, corner sharpness further improving, falloff already reached minimum at f/4.
f/8: Centre sharpness starts decreasing (minimal), peak corner sharpness.
f/11: General, noticeable decline in sharpness; still usable.
f/16: Further, marked sharpness decline. It makes little sense using this aperture, given that DOF is huge anyway. Any DOF increase from f/11 is lost to diffraction.
I had not had the opportunity to test point light sources but from I have seen in the web the lens should be good at it, especially considered the very wide angle of view.