I've got now a cheap adapter, but it protrudes above the camera mount, preventing the lens from focusing to infinity (as well as from screwing in fully to the 12 o'clock position). Some tenths of a millimeter need to be sanded off. What grade of sanding paper (or something else?) should I use?
(And speaking of infinity focus, is it really that important that the lens can properly reach infinity? At such distance, one will normally shoot at a smaller aperture, making the depth of field deep enough to cover infinity anyway, am I wrong?)
it depends on the lens you are using and how you use I think
In some cases you have the one lens that you use only for portraits, and maybe you dont even care about landscapes or getting to infinity, if you then dont even ever need to shoot using only the marking on the lens then I would guess it matters little. Some I know couldnt care less if they lose infinity, they never look at the lens scale, they never shoot in conditions where they cant look in the viewfinder, it works for them and they are happy
What if you were taking pics of the moon?
In your case also its not even just one lens that is off, its every lens that goes on that adapter.
(plus the nag thing of having something that is supposed to work properly but it doesnt, and that you can make to work properly without too much fuss...)
You can start with a 150 or 220 and work finer and finer, dont skip from 150 directly to a 400 though, it takes a lot of time for very fine grades to cut down the scratches of a much coarser grade and you use more paper because u will wear it down before it finishes the job. If its really just a hair to take off you can start with a 320 too, or if you are worried the 150 is too coarse to begin with.
Know that is best to have a light touch and take your time than going ape on it and leave gauges, each gauge is a lot more work to eliminate later on
take a measurement of the thickness at different spots around with a caliper before sanding, if you can check how much you need to take off, slack included
Put the sheet of sandpaper on a flat surface, the flatter the better, marble countertop or glass sheet would be ideal, try to use the best you have at hand. Put the adapter face down on the sandpaper and sand it in a small circular motion or drawing 8s. Do not keep the fingers on the same spot as the pressure is not the same and you will end sanding more on one side, just switch the hold all around the adapter, measure the thickness, repeat until good then finish it smooth, a 1000 or so will leave a nice surface, if you have the tools you can polish it fully
I know many would stop much earlier than 1000 or polishing but polishing the surface is to not ruin the lenses overtime
If you ever think to try it on the camera half way along the work to see if its good or to check if you are actually done before putting work in polishing then wash the adapter well with soap first and an old toothbrush, the suds will carry away every small part of dust, you dont want any of it near the camera body and just brushing it leaves always some, dry well with an hair dryer.
PS: do yourself a favor, remove the spring and replace the screw in the adapter, you wont have to deal with dust going under it or in the screw hole