I record some of our rehearsals and then share with the band. For originals, I think it's a great idea, not only for songwriting and arrangements, but to see how it all fits together in a band context whether we need to add something/take something away/do something differently/etc., it does also show up mistakes, but instead of using it to "point the finger" at someone else in the band, I would hope that we're grown up enough and "professional" enough to realise them, and practice so as to avoid mistakes. At the end of the day, mistakes happen.
In my last "proper" band, we recorded rehearsals for the same reasons, and it worked. The writing got a bit tighter, the mistakes were still there, and it gave us all an idea of how we were "gelling" as a band too.
I bought a Tascam DR-05 a while ago, and it's really good for rehearsals, small enough to fit in a gig bag, but has really good mics and can capture the music well.
Plus, you can share the mp3's with friends and whoever may be interested. It gives them a really good idea of what you sound like as a band.