Just wanted to share a quick story in case anyone else experiences a similar problem:
I love love love my Diva cup but have often experienced irritation starting around day 3 of my period. I made the mistake during my first cycle with the Diva, which caused major irritation, so now I just rinse with water. I do make a point of washing my hands before insertion/removal so I don't get nasty germs in my vagina.
Anyway, I kept getting this irritation and was kind of just chalking it up to hormones or irritation from insertion/removal. This cycle, though, I made a point to wash my hands VERY thoroughly to get all soap residue off....and it's worked! No irritation at all.
So if anyone is getting frustrated with some irritation when using the Diva, remember that it's not just about soap on the cup, but also soap on your hands. I know it's been said elsewhere, but this was definitely my experience. As a rule - if I can still smell the soap on my hands, I rinse more. And I make the water as hot as I can take it.