I dyed mine, just solid colours in the washing machine. Some of them do have a bit of white showing through, not in the pile/loops, but in the base fabric that the loop is woven into, if that makes sense. It's only noticable on my black nappies and even then it's not that bad.
Forgot to add, mine had been used for a few months before I dyed them. I'm not definite that this would affect the dye job, but since they are more absorbant after being washed a few times I would expect that they'd probably pick up dye a bit better after a few washes too.
I'm surprised at that Hanna, mine aren't blotchy at all, it's only if you look closely that you can see that the dye isn't right into the centre of the fabric. I suppose dying new ones would be different though.