Q:

How to win against a moving violation ticket that was issued different than what I had allegedly committed?

I was stopped by an officer that claimed I sped over a 30mph speed limit. When he saw that I have a radar detector, he proceeded to "cut me a break" and gave me a ticket for "failed to signal" (but I did use my signal, and the officer knows it).
He did not use radar (my radar detector would have indicated otherwise) and I was in the lead among other cars. I wasn't speeding, but accelerated faster than the other cars. It seems to me that he realized that he may not have a strong argument in court when he saw my radar. Therefore, I received a citation that was different than the one I was stopped for. 
How would a typical case like this play out in court (generalized)? 
Would he tell the truth, and if he does, would that means the case would be dismissed on the grounds that I did not violate the law in which the citation has stated? (I would probably use "motion to summary judgement" if this happens.)
RESULTS from my case:
First Trial: Officer did not show up (did not give a reason). The Judge offered a continuance to the officer. Case postponed. (NYS penal code states along the lines that if the officer did not give a reason for missing the court date or is not one of the few exceptions for missing the date, case should be dismissed. However, in my case it wasn't. Perhaps the judge had the final say regarding this matter. 
2nd Trial: Officer did not show up. Prosecutor tried to get me to come back. However, I mentioned the continuance is final and that the officer not showing up means there is no witness against me. I got my hearing in front of the judge and the case was dismissed. 
Notes: After going through this ordeal, I realized that the prosecutors were really out to get people to agree to plea bargains. Even going as for as lying to me the officer was present to get me to sign a plea. 

A:

I took my car to the mechanic to have a squeaky brake looked at. I was told it would cost $30. The mechanic fixed whatever the problem was. When I was checking out, they could not find a $30 brake-work item in their computer so they billed it as Tire Balancing $30. Or some such thing. Meh, accounting.
This is not how the law works.
The prosecution needs to prove every element of the crime you are charged with. They need to prove you did not signal. The way this usually works is the cop takes the stand and testifies, and you can cross examine him. Then you can testify if you want to, and can be cross-examined. There might be other evidence against you also, like a dash cam. Assuming there is no other evidence, and that the officer did not prove every element of failing to signal, you do not need to testify. You can tell the judge that the prosecution failed to make the case and ask to have the charge dismissed. Of course, if the judge thinks they did make their case, then you lose. On the other hand, you could take the stand and testify, and subject yourself to cross examination. Just a word of warning, if it's your word against a cop's word, you will lose.
Your best bet is to get discovery, get the dash cam, and show that you did signal.
Be aware, if you get too saucy, the prosecution can add charges. So they could add the speeding charge, but of course, (see above), they then need to prove it.

