Thanks for your input guys.
Yes, we all agree that 1 mm is way to much. I'm yet to confront the guy - I have had a feeling it won't bring anything. However, now that I have another head, I think I'll ask him to do that one properly (I know he has done fine jobs for friends previously).
Thanks for confirming my belief that the copper gasket should be the base one.
@Lucky:
a) I have the Shop Manual, the Haynes and Clymer books and did follow them. I just tried to mess around with the adjustment to see if the clicking sound would change.
b) I'm sure the clicking noise came from the valves (not the cam chain), and only from cyl 1 and 4. I held a screwdriver against my ear and the engine, and it was quite easy to make out where the sound originated from.
c) The idling with the occasional pop you describe sounds somewhat familiar - especially when it was cold.
d) I think the 0,05 and 0,08 makes sense just fine. Those values are found in the Honda Shop Manual. As a european I use metric tools and use the metric values given by Honda. I guess it would have been a good idea if I had added 'mm' in the post.
@crazyPJ: Why do I need 2x1mm when only 1 mm was taken away?