This guy sounds like he very well could be unstable or baiting the range members into doing something stupid.
I say unstable as taunting and making threats to people with wepeons is not a sane thing to do. Maybe a suicide death wish?
I bring the baiting think up as maybe he is anti gun or doesn't like a range in "his" neighbor. Maybe he is tring to get someone to fire a round in his direction or other action so he can try some kind of legal action to close the place down. Seems like drastic action making threats to pursue a legal action, but then again gun fearing wussies never have been logical in their anti gun activities.
There has been some good advice on catching and identifing this idiot, but I think your going to need a plan and lots of help. If the guys sees the trail cams he will either disable them or steal them. If it is not a credible threat and no legal charges can be brought against him you can always try civil proceedings. If you get a restraining order, and he continues to violate that then maybe he can be charged. I usually find that restraining orders aren't worth more than the paper there written on. In some states there are laws about hunter and fisherman harrasment. If your state has these maybe they could be interpeted to protect range activities also.
Stay safe, good luck, and I sure hope this guy gets his nuts cracked.