Here is that particular part of the code, which seems pretty innocuous.
4:22-18. A person who shall carry, or cause to be carried, a living animal or creature in or upon a vehicle or otherwise, in a cruel or inhumane manner, shall be guilty of a disorderly persons offense and punished as provided in subsection a. of R.S.4:22-17. Amended 1995, c.355, s.3; 1996, c.64, s.2; 2001, c.229, s.2.
What is less so is all the surrounding stuff, which is much older. Other parts of the code leave interpretation and enforcement in the hands of the SPCA, who have announced that they will be ticketing cars with loose dogs in targeted enforcement areas. At least one legislator has said that he didn't agree that the bill allowed such a loose interpretation when he voted for it, but the other (preexisting) parts of the animal cruelty law in 4:22 clearly vest that authority in the SPCA.
, I looked at the NJ SPCA web site today and they seem to have taken down their whole "vehicle safety" section, which I think was where they had announced their intentions. Paul Mulshine of the Newark Star-Ledger has had some interesting coverage. He's a political columnist with a certain point of view that must be factored in, but he finds some interesting stuff.