A few tips that can give you a better chance to not be around belligerent or violent fans or get harassed at NFL games.
1. Avoid going to games where the opposing team has a huge fan base. This is probably the biggest factor of anything else by far and no one ever seems to notice. (Cowboys, Steelers, Bears are a few teams that come to mind)
This has nothing to do with people that are fans of these teams (Im a Cowboys fan), but they bring so many fans to the home stadium that it can split the stadium from anywhere to a 70/30 to 50/50 split. I was at the Bears vs Cardinals game on MNF (Dennis Green "they are who we thought they were") and I can tell you first hand that on the lower section there were more Bears fans in Arizona in some sections than Cardinals fans. This makes belligerent people feel like they have more security because they have a bunch of "their" people around them to protect them. And Cardinals fans aren't going to take smack talk on their own turf, so things can get out of hand rather quickly, especially when the Bears come back and win the game. I saw/was around more fights on that one night than any night of my entire life, including college and bar crawls. Also, never go to a game where the Eagles are playing, just don't.
2. Buy lower seating and sit as close to the middle of rows as possible. The first one is a no brainer. The closer you sit, the more money someone paid for the game. This can mean two things. They are more likely to be older, more mature, and more educated. This means less likely to get into an altercation. This can also mean the fan has a more invested interest in the game since they spent more money on the ticket, and will be more careful to avoid getting kicked out.
Sitting in the middle of the row means there are less people that walk by you every time that the drunk idiots have to go piss for the 10th time or pass over cash to get another beer or pass by you again spilling their 12th beer on your sons jersey. Plus, some drunkies always try to hang out in the entrances because they are having to go get more beer or piss so frequently that they just hang out there until a stadium employee has them leave. Less interaction with drunk idiots, less chance of altercation.
3. If you are an opposing team fan, tone it down a touch. I'm not saying that you shouldn't cheer for your team, you should have fun and absolutely do that. But you shouldn't bad mouth the opposing team, or openly complain about Refs. Those things usually end up with someone saying something back. Wear a Jersey, but don't paint your body or bring unnecessary attention to yourself. You are just asking to get harassed.
I have only been to about a 1/4 of the NFL stadiums, but these things seem to hold some weight. Most people at games are cognizant enough to realize their is a kid sitting beside them and not to drop a F bomb every 5 words. But there is always going to be that dude, and at the end of the day it's just a crapshoot if you are going to get unlucky enough to get a group of them. If you do happen to get in a group of these idiots, tell a security personnel right away when you feel uncomfortable, obviously not in front of them, so that security will pay a little extra attention in your vicinity.
Overall, I would recommend taking your son to a game because it's something he will remember the rest of his life and I still feel the pros outweigh the cons.