Don’t you just hate it when you see this dreaded image in the place where a YouTube video is supposed to be embedded? If you consistently have this issue, then there is a fair chance you have your YouTube app hidden via a jailbreak tweak, or you have restrictions enabled. Restrictions can be enabled without a jailbreak.
As it turns out, having the YouTube app hidden can result in embedded videos being replaced with the image above. YouTube videos on the actual YouTube site will still play fine regardless, but embedded videos can give you problems if your stock YouTube app is hidden, or you have restrictions enabled.