Should one mention multiple, albeit somewhat unrelated research interests? As the question implies,  I have two main research interests in the natural language processing and computational genomics domains.  While I have a preference for the former,  I am also very interested in the latter.  I ask because I am not sure if it would look like I am too unfocused for a PhD. Many professors seem to have multiple areas of interests,  some of which are not too related, but nonetheless I want to make sure that mentioning multiple interests will not hurt me.
If you can convey your enthusiasm for the overlap of these two somewhat distinct areas, you will be ahead of the game. A PhD candidate is expected to extend the limit of human knowledge, and one of the better ways to do so is to research within the overlap of two (or more) disciplines. I would tend to see having more than one area of interest as being an advantage rather than a disadvantage. Of course, as your question implies, a multiplicity of interests can backfire by causing a candidate to appear unfocused. Focus on the overlap, and make your application shine!