I wash mine with Woolite when I think it's necessary, or even just drop it in the washer wet with shampoo mix. But I hardly ever bother washing mine since they rinse clean during the carwashing, and I don't bother hanging them up to dry very often either. Seems like the ones I treat oh-so-carefully don't last any longer than the ones I just rinse out and lay over the rim of the bucket :nixweiss It's kinda like the individual variations between different mitts matter more than how I treat them, not that I think the latter is unimportant or anything.
I dunno about MF shampoo...somebody once posted that they contain degreasers, and I wouldn't think that too great for keeping the fur stuck to the pelt. Drying out the "skin" part of it with a harsh product might hasten the thing's falling apart.