Sounds like maybe there is mold inside? Bleach will kill mold. I guess I would experiment with mixing a mild bleach solution and putting it in the iron, steam a little with it, let it sit overnight (mild bleach solutions take awhile to work completely on mold), empty it, rinse it out and steam some more, and see if that takes care of it. While letting it sit overnight with the mild bleach solution in it, I would also sit the iron in a shallow pan of mild bleach (to let the bleach stay in contact with the other side of the holes). This would void the warranty, but I haven't found warranties to be very helpful with irons anyway.
If you are wary of the bleach, you could try full-strength vinegar instead for the overnight soaking.
If it's not mold, then it could be an accumulation of mineral deposits. This happened to my Rowenta, but the mineral deposits were white. Even full-strength vinegar seemed unable to take care of it (although at the time I hadn't thought about letting the iron sit overnight in vinegar so it could reach both sides of the holes). I ended up using some product used to clean mineral deposits out of water softeners (I think it was Rust Out, although what I used was a powder not a liquid). I ran it through the iron a few times as if it were vinegar, rinsed the iron, etc. I still had to use a pin to flake off some of the thicker white mineral deposits in some of the holes, but together that got the iron working again.
I should mention that my Rowenta has a built-in water tank. If yours is the type with the separating water tank, I'm not sure that the above will apply.