It's not that you can't access it. It's just that the web interface was not designed for mobile devices and is extremely clumsy when being used on one.
Even if there was just a mobile version, instead of a dedicated app, it would be worlds better. Although, I do have to say that getting push notifications about tickets that weren't through email would be amazingly slick, and shouldn't be too hard using something like jQuery Mobile or Phonegap.
**Edit: I do realize that this is an old topic, but I believe that it is still relevant.