I have been told that brown dirty stuff in the corners of cat's eyes can by a symptom of ear mites. Treating the ear mites (medicine in the ears, and then massaged a bit, repeated after some time) can clear up the symptom showing up in the eyes. I am not saying this always the reason, but the dark brown stuff, I believe is more likely to be mites than just regular clear or neutral colored stuff.

One way to check, of course, is to look deep into the ears, and see if there is brown stuff there as well. No Q-tips! but some massaging is needed with the medicine to break up the waxy stuff the mites are living in.