Recently I forgot to switch to ND 32 while filming in bright sunlight (I was using ND 6 instead) which gave me an aperture between 6 to 8:
Though I am quite familiar with the laws of optics I did not expect the image getting so poor (soft, that is) compared to open aperture shots. Could this considerable loss of sharpness, to some extent, also be caused by the A1's ND filters? What are this filters made of, by the way?

No, I don't think the ND filter caused any of the softness, it was simply the iris being closed near to the max.

With small apertures the diffraction starts to play a role, more so with HD resolutions. Try to avoid stops smaller than f5.6.

With a 1/3 inch sensor 1440 pixels wide the sensor resolution is around 100 lines/mm (200 pix/mm). To get good results the lens must be extremely sharp. That conversly means that diffraction kicks in earlier than in large format video or photography.

Of course using filters never makes the picture sharper either, but ND is the lesser evil.