Not sure about NYC, but we have gotten quite a few salvaged cars over the years. Between my father and I we have gotten a first year Mitsu Montero, early 90's Saab Turbo, 1996 Audi TT, 1997 MB E300, 2008 MB E350, 1998 BMW 325, 2008 BMW 335XI, 2008 MB SL550
We have never had a problem with any of them that we attributed to being salvaged. For example, My TT threw a CEL, and it was due to a well known problem that was fixed for free.
We drove the Saab till it died, Mitsu was sold to my uncle and is still being used, TT was totalled, (which was my bad), MB E350 is being used, as is the E300 and the SL550; BMW 325 was rear ended, and the 335 Xi is my sister in laws.
Best thing to look for is something that didn't get bad structural damage. Theft recoveries can be best cause if it was just joyridden once, you prob will be ok.
If you want the website for the guys we go to, PM me. They used to be based in the Bx, but moved to a bigger lot in Patterson.
PS. The last car we got was the BMW 335XI and the MB E350 in the last 2 years. we have built a very good rapore(sp?) with them, and they aren't shady.