I am also getting mixed results with COUNTA.
It seems if the cell is totally empty, it is not counted. But if there is a formula in the cell (like IF(Something,"Name","") which returns a blank, it is counted.
My workaround is to use COUNTA-COUNTBLANK
COUNTBLANK does seem to work correctly, and counts the number of blank cells, so subtract it from COUNTA.
Please send feedback to Apple about this at
http://www.apple.com/feedback/numbers.html
so they can get it fixed.