Could also be mineral deficiency.. Is she bred? Late gestation really seems to bring on mineral deficiencies. Heavy parasite loads can also cause coat trouble...or, at least, that's the common wisdom.
I'd probably just make sure she's got good loose mineral and deworm her with ivermectin. Ivermectin will kill external parasites (lice/mites), too, if she has any. To make sure you get externals good, repeat the treatment in about 3wks..
If she's not had good mineral to this point, you might do some research on copper bolusing and Bo-Se.. You might also consider drenching her with a product called Red Cell for about a week...it's basically like highly concentrated, highly bioavailable liquid vitamins and minerals.
Something else to consider is adding a bit of black oil sunflower seed to the diet.. Like, a handful at a time.. If the wether isn't having any coat trouble, keep him out of the sunflower seeds as they're pretty high in phosphorus.....unbalanced phosphorus + male goats = bad times.