Q:

What is this insect with rough brown shell on potatoes?

This insect with a rough brownish shell showed up on potatoes at a friend's house in Vermont. I've looked around in books and online and can't find anything that's an exact match. Current control strategy is knocking them into a can of soapy water. (My friend hasn't said anything about them making a stink when removing them.)
Update via email:

Yes, I've had a couple fly away.  Though they're very slow to get moving
  (i.e. very easy to get into the soapy water first).  They're really stuck
  to the leaves, so I have to really scrape them off the leaf.  You can't see
  in the pic, but they leave big round holes (size of pencil eraser at their
  biggest).

A:

It is a Tortoise Beetle (part of Leaf Beetle subfamily), probably Plagiometriona clavata - Common Garden Tortoise Beetle or Clavate Tortoise Beetle.
(The beetles as a group seem to have undergone a number of taxonomic and name changes)
See another excellent picture of one here: http://www.pbase.com/image/28969283
There is some more information about them from the University of Florida here:
http://entnemdept.ufl.edu/creatures/orn/beetles/Plagiometriona_clavata.htm
Also, anyone interested should google image search "tortoise beetles" because they look amazing :D

