I've a little patch of irises which have been fine for a few years but
the weeds growing between them have become almost impossible to
control so I resolved to dig the whole lot up (I realise this might be
a bit late in the season) and replant.

A lot of the rhizomes have broken off a developing plant. See pic:-

http://dl.dropbox.com/u/10508583/im%201.jpg

-should these simply be discarded or do they have a future for a new
plant?

Here is a pic of a new devloping iris.

http://dl.dropbox.com/u/10508583/im%202.jpg

I noted in one youtube video the presenter trimmed the long roots
quite short. Is their any advantage in doing that?

I have quite a few of these

http://dl.dropbox.com/u/10508583/im%203.jpg

- which are tiny and without any rhizome to speak of. Do these
normally survive being dug up and replanted?

Many thanks if anyone can offer some advice...