How do I see the dock in a fullscreen window in OS X?
It appears that the trick is to move the cursor to the bottom of screen like I normally would, but KEEP MY FINGER ON THE TRACKPAD when I get there.  If you take your finger off of the trackpad, the dock won't appear, but if you keep it there then it will.

(There are other reports that moving the cursor to the bottom of the screen and then repeating the same action again can make the dock appear, but I had inconsistent results with that technique.)