What is the "shadow" that appears to go across the plane in a very irregular manner? Is there a local dust cloud obscuring parts of the main plane?

It's the Great Rift http://en.wikipedia.org/wiki/Great_Rift_(astronomy)

Interesting, I haven't seen this clustering from looking at the sky before - is it because this is more sensitive than the naked eye?

This is one of the downsides of living in a heavily populated area. It's quite visible once you get away from the light pollution around cities.

It's called the Milky Way!

In general, you can't see it if you're anywhere near an urban area.

You can see it in areas with little light pollution (although not quite like this image), otherwise most of the stars are too faint.