stephen it could be the food you are feeding, an allergy the animal is suffering from. It could be just plain old dry skin, or other skin ailment. If the dandruff shows on the coat and when you reach for the hairs it is caught on and run it through your fingers and it vanishes, it is dandruff. If the spots stay after you run your fingers over it then it is lice. In that case a vet visit is warranted. Also if your reach for the hair and gently pull and the hair comes out in your fingertips, you should call your vet and ask him or her to recommend a good shampoo for you to use.
If it is dry skin, you can do a few things. You can try using a humidifier in the house, suppliment the diet with omega 3 fatty acids, or start feeding a food that's high in the omega 3 fatty acids. DVM makes a shampoo that also helps with dry skin. It's called Hylite, but you would need to get it from a veterinarian or online.
Just be sure to make sure it's just dry skin, and not an underlying problem
My Simon gets dandruff sometimes too. I know his is caused by dry air. We live in Florida, so the air conditioning runs almost constantly. When he starts to get dandruff, I turn off the air and open the windows every day for a little while and it goes away. A humidifier is a great idea in the winter.
Thanks for all the suggestions! The cat in question is not mine, but that of someone who adopted a cat from me and my cat rescue group. I'll pass on all the info. Thanks again