Sounds like he was convicted of a misdemeanor domestic battery which certainly is a crime of domestic violence. Background checks on police officers are usually far more extensive than that on regular citizens in that the police agencies have access to the criminal justice databases that the public at large would not have access to, e.g., NCIC.
The Lautenberg Law may impact him although I understood that police officers won a case striking the law as it applied to them in one part of the country--but I don't know how the case ultimately ended up. That may be his biggest concern because it is going to be difficult being a police officer if he is disqualified from carrying a firearm. If he qualifies, he might look into getting an expungement as this should serve to restore his firearm possession rights if he is disqualified under the Lautenberg Law.
A nolo contendere plea has the same effect as a guilty plea for purposes of the criminal law as under a nolo plea the person is not contesting the sufficiency of the State's proof regarding what they are charged with and under the guilty plea they are admitting that they are guilty with what they are charged with. A nolo plea does not hold the magic that some people think it has.
Here's a link:http://www.saf.org/LawReviews/Pressler.htm

