I bought 2 years ago. In my case, I think that the broker had a lot to do with the sale, and that if it had been offered FSBO I might not have made an offer. This may be an unusual case though - because the broker lives in what is now my building. I got a good sense of her as a person and determined via instinct that because she had lived in the neighborhood for so long -- mostly in a different (and high-end) building, she would not have bought into this current building if it were questionable in any way. Also I knew she was familiar with the board and would be able to help me with the package. I closed in under 3 months.
So, while this is an unusual case, I do think that there are lots of potential buyers out there coming from Brooklyn and Manhattan who are relying on what they feel is a trusted source (a broker who has been selling in this neighborhood for years and years) to advise them on what might be a good or bad building. Of course this may not be the best idea - for a buyer to rely on the broker for such info, since the broker works for the seller- but I believe this happens pretty frequently in terms of buyer's psychology. Also there are at least a few brokers in the neighborhood who probably won't take what they feel is a questionable listing such as one that is overpriced or in a building with bad finances, because they have a reputation to uphold.
And a good broker will also have a list of people who are waiting for the right apartment to come along. Those same people might be reading the NY Times classifieds every week to see if there is a new listing like yours, but they also might not.
However, I see that you could probably save alot of money by doing it FSBO if it works out. Would it be possible for you to list it FSBO at first and see what happens and if you are not successful then turn it over to a broker?