Hmm, interesting.  I did not get a reply so I took the bottom plate off
the camera and removed and disassembled the button.  There is no
adjustment on mine. No set screw.  I have the C330f if that makes a
difference.

I solved the issue by glueing a couple of small pieces of plastic to
the bracket that holds the outer part of the button.  This reduced the
travel of the outer button, the cable release now reliably trips the
shutter.  

Points to note where:

1.  The small screws that hold on the bracket for the shutter release
   are longer and thinner than those holding on the bottom plate.  This
   is not obvious as they are so small.
2.  There are a couple of inexplicable copper washers between the base
   plate and the metal 'frame' of the camera on some of the screws.
3.  There is a very inexplicable small strip of aluminium acting as a
   packing piece which would not be needed if there were an equally
   inexplicable recess for it to sit in.
4.  Either you get no superglue out of the tube or too much.  If the
   latter it gets into the wrong part of the button and you have to
   clean it out!

I have no idea what the washers or the bit of aluminium are for.

Will do.

Replacing the light seals are the next job.  However I plan to use it
over the next week and it does not leak light - yet.  A job for when I
get back.