To give this a bump/info, it seems Youtube videos no longer work on profiles. I don't know if it's from a glitch or what.
Well, looking around, apparently it's broken for some people's profiles, but not all. I'm guessing the way the codes work updated somewhat, so those done a specific way end up breaking now? I have little clue how coding works, so someone else probably has a better answer.
Edit:
GOOD NEWS EVERYONE! I discovered a fix, and simpler code for embedding Youtube Playlists!
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<div style="float: left; margin: 3px"><object type="application/x-shockwave-flash" style="width:188px; height:26px;" data="//www.youtube.com/v/cON4bkq5xpc?color2=FBE9EC&border=1&rel=0&loop=1&autoplay=1&showsearch=0&showinfo=0;list=PLlirgeHmmztqyCG3GpxWIEMRJGf5UhkJp&version=3">
<param name="movie" value="//www.youtube.com/v/cON4bkq5xpc?color2=FBE9EC&border=1&rel=0&loop=1&autoplay=1&showsearch=0&showinfo=0;list=PLlirgeHmmztqyCG3GpxWIEMRJGf5UhkJp&version=3" />
<param name="allowFullScreen" value="true" />
<param name="allowscriptaccess" value="always" />
</object></div>
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Orange is the ID of the first video you want to play, found in the Youtube video's URL.
Yellow is the playlist option, which is where you place your playlist ID (the limegreen example here). You can find the playlist ID in the URL as you're playing videos from the playlist.
If you want to embed only a single video, just remove the ";list=" and playlist ID. Easy as pie.