It is lawful to arrest you based on a mistake because the courts have said it is. It is also lawful to not accept your claimed proof as absolute. You provided it. It could be altered. They are allowed to use proof available directly from the court records. If that wasn't available at the time, they can continue with the known facts on hand.
As to my belief the issuance of a warrant must be based on probable cause;
its not my belief. It's the law. The 4th amendment;
Amendment IV
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
i presume the warrant was issued by the municipal court and not the family court. Is that correct?
As to you suspecting people arrested not having had dealings in court and not having the warrant dealt with then; you would be incorrect. There have been people arrested for a crime, put in jail and subsequently released and an outstanding warrant the entire time for another crime not be known by the parties involved. The systems we have in place are not perfect. Crap happens.
I suspect you need to address the current matters before running off thinking you have some major civil rights claim. You may be surprised what happened is not improper at all.
If if you find it is, then go back to where I said; mistakes, as long as there is a reasonable belief the actions are correct, won't result in you having a winning ticket to the lawsuit lottery.
Read this:
http://www.state.nj.us/lps/dcj/agguide/dvpolrsp.htm
I see nothing stating an arrest warrant is automatically issued upon filing for an RO.
you can also go here and read where an arrest is required. Section 3.4
http://www.judiciary.state.nj.us/family/dvprcman.pdf
you have also said nothing about the person making a domestic violence complaint but simply filed for a restraining order.

