How can I finish the tops of my balls so the stitches are not so open in appearance?
Here is an amazing tutorial for how to close amigurumi shapes. It's a bit of work but the results are beautiful. 

Essentially, this method works by creating an identical system to your opening magic loop (if you're using the magic loop start), by adding a drawstring to the last circle of stitches. This drawstring can then be pulled until the circle is completely closed and then tied in place and finished off.



As laid out in the tutorial, the steps are:


  
  Decrease the opening in your work until you have 6 to 8 stitches or less.
  Thread a tapestry needle with the tail left from your work. Insert the needle under the next front loop.
  Repeat for the remaining stitches pulling the yarn lightly.
  Pull the yarn tightly until the hole closes completely.
  Insert the needle under a loop close to the closed hole. Repeat one more time.
  Pull the yarn until creating a loop and insert the needle into the loop. Pull the yarn creating a knot.
  Insert the needle into the closed hole and make it come out as far as possible.
  Pull the yarn until the knot disappears into the piece. Cut the yarn close to the piece, the end will disappear inside it.
  Piece closed.