What sort of diet is kitty on? Not being any sort of expert this sounds like a vitamin deficiency of some sort but I'm sure Opus or Jade can answer better. The more info you can provide the better-is kitty weaned, diet, stress factors, other pets, etc. Good luck w/your little guy!!
Is his skin red or swollen? Is he scratching a lot? Maybe he has scabies, it's really easy to cure if that's the case. I doubt that it's a vitamin deficiency because he should be drinking milk from his mom being that small, and milk has everything kittens need. If he's already eating other things, as long as you give him food that's for kittens he'll be ok (with the diet stuff).
You should take him to the vet because most scabies can pass to humans and trust me, you don't want them!!
One month is a little young to acquire a kitten. It sounds like malnutrition or the wrong nutrition. If I remember correctly I gave an orphan kitten egg yolk as well as milk. Cat milk has a very high protein content. Also young kittens cannot defecate or urinate without being massaged, but I can't remember until what age you have to do this. Speak to your vet.