How old is the machine? are you sure it is washing powder?
I'd think it's more likely (especially if you live in a hard water area) it's spots of lime scale that has built up in the machine and is flaking off during the wash
Try running a load with no powder in it at all and if it still happens then it's not the powder.
if it is limescale you could try running an empty load with one of the descalling products, but if its really bad then a machine strip down and clean may be the only option (not a easy, quick or cheap job!)