Get rid of duplicate "problem types" in browse mode

Summary:
Be more in line with how debug mode shows debug info, and store
everything extra related to browse mode in a separate div

Test Plan:
Do a couple exercises in browse mode, notice that the "Problem
types" header and buttons aren't duplicated.

Reviewers: eater, stephanie

Reviewed By: stephanie

CC: alpert

Differential Revision: http://phabricator.khanacademy.org/D2049