On Fri, 17 Sep 2010 06:31:05 -0700 (PDT), "
wrote:

Ok, so I'm probably making more of this than I need to ...

I am replacing outlets to match new paint in a room and did not notice
that one electrical box still has the old screw in the bottom hole ...
evidently it broke in the hole. There is nowhere to grip it on either
side, not even with needlenose pliers. The plies basically slide off
as soon as I go to turn it.

Can I take a tiny drill bit and drill it out or is there an easier
way?

It has probably been suggested already, but I didn't read the replies.
You can try to grip the screw inside the box and twist it where the
screw will run into the box and fall out.