To explain a point on this question, I made a video at screenr.com and linked to it.
I tried to use
embed markup, but it was just ignored, which is a good thing because it would not be a safe solution.
But it would be nice if Stack Exchange found a safe and easy way for users to create quick screencast videos just as they did with pictures. The best solution would be like the new photo upload button, e.g. a "full-screen video recording button." Perhaps SOIS could outsource/partner with a company like screenr.com or YouTube or Jing to make this possible?