Wiki front-end edit produces a messed up page

The front-end edit produces a mangled page with two edit areas, and pushes down the navbar to below the first edit area. I've tried different themes (including Twenty Thirteen) and have verified that it's not a conflict with a theme. Here is a screencast to show you exactly what I'm encountering: https://dl.dropboxusercontent.com/u/105481589/wiki-frontEnd-issue.mp4

How can I get this corrected?