First of all it is not the police that made the mistake, it was the Court. You can try to clean that up. There would be no entries without some type of plea in the Court. But more information is needed. How did this come up? Why would a juv. disposition cause such a reaction at this time? Call with more information.
Obviously somebody made a mistake at some point. Either the Court entered the conviction improperly or your representation at the time did not effectively communicate to you the actual charge against you. You will need to provide more information and you should consult with an attorney. Depending on how much time has passed, you may be eligible for an expungement.
you can sue the pope if you have the filing fee- the question is will you likely succeed- the police will have all sorts of immunities and in any event probably aren;t responsible for the entry of the record.
Something doesn't add up here, that's for certain. Your record likely has a conviction for N.J.S.A. 2C:39-5, which includes a number of firearms types, from machine guns to BB guns. As that is the case, it may explain why your CCH says "possession of a machine gun." Then again, possession, as a juvenile, of a 4th degree offense for possessing BB gun probably shouldn't bar you from being a responsible gun-owning adult.
I suggest hiring an attorney to help you get the records corrected, or expunged. If you can't afford an attorney, contact the Essex County Bar Association.
The foregoing is not legal advice, and nothing in the foregoing shall be deemed to create an attorney client relationship. If you feel you need to speak with an attorney regarding your issue, it is recommended that you contact an attorney with expertise in your area of inquiry. The information related above is purely for informational purposes, and should not be acted upon without speaking with qualified counsel familiar with you specific situation and the laws related thereto.