From what I've been able to find out about the NHS on our campus, anyone whose GPA is high enough (don't recall what the cutoff is) is invited to apply for membership. Then they look at the applications and assign point values to things like community service hours, school activities, positions of leadership, character, etc. Students must achieve a certain point level before they can be tapped for membership.
OP, your son sounds so much like mine - and we had the same thing happen last year when he was a junior. DS got off to a slow start but has become very involved, is on advanced diploma so takes upper level courses, has never been in trouble - no disciplinary referrals EVER - great student. He has been invited to apply for NHS every year since he was a sophomore. That first year, the students had to get signed letters verifying the community service hours so we decided not to turn in the application. DS had not done anything that could be counted as community service nor was he very involved in campus activities at that point. Well, lo and behold, they decided not to weigh that as heavily and lots of kids got tapped even tho they didn't have the cs hours & such that were supposedly required. Last year DS was much more involved in school activities, holding leadership positions in some, but still hadn't done a lot of "official" community service. Based on how things turned out the year before - and the fact that they were no longer requiring the verification letters for cs hours, he decided to give it a try anyway. Well, he was turned down on the basis of not having community service OR leadership stuff.

This year, he was once again invited to apply but he decided it just wasn't worth the time it takes to fill out all the paperwork - he's a little busy being editor of the paper, section leader in the band, etc. Besides, he already has a scholarship that pays full tuition for 4 years of college so we're not sweatin' the small stuff. Don't mean to sound snide but obviously the folks who choose NHS members at our school overlooked a gem. Their loss. Based on our experience and some of the other posts on this thread, I wouldn't get too worked up over your DS not getting in. Obviously NHS membership isn't all it's cracked up to be.