To beat a speeding ticket in NY City you will need to do one of two things:
1) Hire a lawyer with an “in” at the court. Expect to pay through the nose.
2) Appeal the ruling to a higher court. Good luck with this as an appeals court will only review the proceedings and the decision of the traffic court. It will be difficult to stick anything into the court case that can be used in an appeal (see next paragraph).
NYC courts are “kangaroo courts”. That means they exist only so that you can exercise your right to fight the ticket – and lose. There is no prosecutor, so the judge or the cop has to act as the prosecution. Since it is unconstitutional for a judge to do this (judges must be unbiased), they have adapted the style of the court session to be a “complaint” so that the cop is bringing a “suit” against you and you are not being prosecuted. Forget about trying to win, or asking them to show records of the radar calibration – you are guilty a priori.
Outside NYC, it is common for the courts to entice you to plea bargain – more money for them, less points for you. Most of the time it is more advantageous to accept this than to annoy the court by fighting the ticket (unless your case is iron-clad).