*  8 mesh is recommended, but 6 mesh harware cloth is cheap and strong
   and widely available.  Is it satisfactory?  Or does the mesh need
   to be finer?

Speculation is that 8 mesh may be unnecessary and is only used because
that's what's used in other equipment (like escape boards and double
screens).  Again, speculation is that 6 mesh would be an improvement,
as it's more readily available and will allow more debris to fall through.
This speculation is in need of field testing.

*  Is a bottom entrance necessary?  Some of us have auger holes in the
   brood boxes.  Would they suffice for entrances?

Bottom entrances are man-made devices.  Auger holes should suffice.
Cracks in walls work for feral bees, as do holes in logs and hollow trees.
Bottom boards are not used by some commercial operations who simply
put their boxes directly on pallets.  Seems to me the main benefit in a
bottom board is for the beekeeper.

*  Does debris build up on the screens?  Is there wax or dead bees
   after winter?

Yes, although I can't comment based on personal experience other than
I once bought some used equipment that utilized home made screened
bottom boards with window screen (don't know the mesh number).
There was a lot of crud in those bottom boards, including a well
preserved mouse skull.  Goth bees?

*  Has anyone noticed any adverse effect on spring build-up?
The guy who I bought the equipment from (who had used screen
bottoms for year (decades) before the came in vogue claims not
adverse effect on spring build-up.  Also claims not noticable benefit
in varroa control.  Last research I saw claimed the varroa population
builds slower, but still gets above the "economic threshold" by fall.

Aaron Morris - not thinking of investing a lot in screened bottom boards.


allen
http://www.internode.net/HoneyBee/Diary/