Crusher,
Welcome to SDN! I'm a graduating student who will start my ENT resdidency next year (or, at least, the general surgery part of it).
First off, it sounds like you're pretty interested in ENT, which is great. The specialty is, as The Throat pointed out, quite broad in terms of patients (young and old, healthy and sick) and medical conditions. Some of the things you treat include peds (tubes and tonsils, foreign objects, congenital malformations), head and neck cancer, hearing loss and related neuro-otology, sinus disease and allergies, facial plastics, facial trauma, voice/laryngology, snoring and sleep apnea, and thyroid/parathyroid disease. The variety of different procedures you can perform is dizzying, and it is extremely difficult to master all of the diverse surgeries.
The perception by some that ENT is a narrow field is a combination of a lack of exposure to the field on the part of most medical students, and the fact that ENT is a specialty that you choose right out of medical school. In many other surgical or medicine sub-specialties, you first do a more broad-based residency, and then specialize during your fellowship.
As far as competitiveness, I would focus less on board scores (which you can't change now anyway) and more on the things you can do now to improve your application. Good letters of recommendation from known ENT faculty, research (does not have to be ENT), and good interviewing skills can go a long way.
As for your away rotation, I did mine in August as well, but I sent in my applications the first week of August (~2 weeks before the "Target Date"). Thus, I didn't send my away recommendation with my application. I highly recommend mailing your application early because I know people who were contacted after submitting their application that something was missing. It can take weeks to resolve these issues and get your application on the road. You can always send an additional letter of recommendation from your away rotation later (but you will have to send it directly to the schools).
I hope that answered some of your questions. Good luck!