slideToggle height is "jumping"

The quickest fix in your case:

.message_container { width: 361px; }

I'm not sure exactly why, but not giving the container a fixed width when containing a <p> causes issues, give it one and the jumpyness goes away.

I found this problem in many occasions in which I was animating just the height with slideToggle but not the margin/padding.

So, something like this might solve it:

$("#thediv").slideToggle().animate({"margin-bottom": "toggle"});