I've been using the Webupd8 PPA for months without problems.
Let me add two points:
Unity gobbles up Sublime's menu (which I like, because it means I can use the distraction free mode without the menu showing). Unfortunately Sublim doesn't know that this is happening and it renders the tabs twice. The simple fix is to switch to and from fullscreen (hit F11 twice) and everything is normalized.
If you change theme, it's often a good idea to restart the editor for the graphics to sort themselves. (This is the case with other OSs as well.)
Hope this helps,