Coming from inside this department, I must respectfully disagree with Ondine--basically, there's nothing more you can do at this point but wait. Hopefully they told you your ranking on the waitlist (right?), and this is not something you can change, insofar as it was designated by the whole admissions committee (which putatively won't be meeting again). Historically, I think the first, second, and often third person on this particular waitlist can pretty much expect to get in, albeit sometimes not until maddeningly late (i.e., after April 15); beyond those, it becomes more a matter of luck.
And speaking of luck, I wouldn't attribute this result to any deficiency in your application, problem with your interview, etc.. The fact that you got to the final round means your application was very, very good, and if you thought the interview went well and got a nice response to your thank-you email, I seriously doubt that it had any negative impact--although this is the first year that NYU used them, these things tend to be more about weeding people out than making fine distinctions among those who survive them, so as long as you seemed minimally cogent, mentally stable, etc., I doubt it had anything to do with the eventual outcome. When only the top 4-5% of an enormous applicant pool gets an offer, it often comes down to completely stupid factors over which you have no control. Maybe they had someone else who wanted to work on Dante and who they liked slightly better because s/he already had several publications, maybe there were several finalists with a background similar to yours in some other salient way (languages, home-country/region, education...), etc.. Whatever it was that tilted things against you, it certainly was *not* that your interviewers returned to the committee and said "ah, he looks good on paper, but such an accent!", and almost certainly *was* something about the constitution of the final applicant pool that has nothing to do with their judgment of your qualifications. And if your app is half as good as your English, I bet you'll get into Columbia no problem.
So, as Ondine said, don't despair. And depending on your waitlist ranking, you are more or less likely to end up with a very difficult choice sometime in April--there are ALWAYS people who say 'no' to these offers.