Alan,
I'm not 100% sure why the captions box isn't showing up in your example. It's working well on
http://mediaelementjs.com/ so I'm not sure what's going on in the example (the volume slider isn't working either). This is using :hover commands, but perhaps I should change it over to JavaScript to make sure it works in wonky scenarios.
In regards to the fullscreen playback, here's what's going on: since you're using MP4, Firefox has to fallback to Flash or Silverlight. However, those plugins don't let you call the fullscreen command from HTML/JavaScript, so you have to click a second button on the Flash player. I wish I could change that, but it's just browser/plugin security stuff.
Alternatively, you could provide a WebM file and you'd get the full HTML5 experience in Firefox and Opera.
JD