Having similar errors. This happened on a previous site I was working on, then seemed to stop. This time I lose the scroll bar on the right and have to tab through content, which gets messed up too. Attached is a screenshot of the stuff that happens. I would love to get this figured out.
Wow, that looks pretty messed up - can't say I've ever seen this behavior... Can you replicate this on a fresh installation as well? Might be inconsistent sitetree records causing markup breakages. You didn't overload any CMS templates right? Do you have any modules installed? Can you please try admin/?flush=1?