@chris94chris94,
It's difficult to say how this incident might affect a future application to the NYPD because it hasn't yet been legally resolved. I'd suggest you wait and see how it turns out rather than worry about it right now.
Your mug shot and fingerprints mean nothing in terms of affecting your application--just the fact of an arrest means very little. The NYPD will also take your fingerprints as well.
Apart from criminal behaviors, the NYPD looks closely at personality issues--they do try to weed out those with personality traits that might be problematic in a police officer. In order to do this, they administer personality testing to applicants, and they scrutinize the applicant's past behavior (in school, on jobs, in the military, etc.) for anything that might be suggestive of problems. In that regard, the incident you refer to might indicate you are somewhat impulsive and can become aggressive when provoked. Those are not desirable traits for an applicant to have. If such things are generally true of you, you might want to give more thought to your own suitability for police work.
Being charged with possession of a fake ID does not exactly jive with your self-description as a completely moral person--it suggests you misrepresent yourself in order to evade compliance with laws. That's not exactly a selling point in an NYPD applicant.
Regardless of what happens with your current legal case, the NYPD will consider it in the total context of all of your application materials in determining what weight to give it. In the context of everything else they know about you, it might raise red flags, or it might not.
And, should your application be rejected, for any reasons you feel are unfair or unreasonable, you can appeal their decision, and the NYPD has an extremely fair and unbiased procedure for review of such appeals.
So hope is not yet lost as far as your potential acceptability to the NYPD is concerned, but your current legal problems should serve as a wake-up call to you that you'd better display better self-control from this point on, and stop skirting laws with fake ID's, if you really want to make the cut and get accepted by them. It's not just criminal convictions that could cause your application to be rejected, it's also the patterns of behavior you display.