The biggest threat to the stability of the NFL is probably player safety issues. It's seems like every other day a new group of players are suing the NFL. I mean, they probably should. Even if they have no case and even if they get nothing from the suit, the case itself brings attention to a major problem that needs to be addressed for this league to survive. Also, I'm glad to see that major steps are being taken outside of the NFL too - at a peewee level in particular. A new culture of safety needs to sweep through the football playing community. A new culture should sweep through.
And to Roger Goodell's credit, he seems like the type of guy who wants to bring about this culture change. The man has a lot of faults (lol referee situation), but this isn't one of them. His rigorous attention and dedication to player safety is incredibly important and quite admirable.
That being said, the change needs to be brought about in a way that doesn't fundamentally alter the game. Personally, I think this can happen through three major methods of change. First, player education. The independent concussion evaluators are a great addition to the game. Their presence emphasizes the necessity of putting health first - even during game time. As more and more players learn that their health is priority number one, we should see long-term health problems decrease. Secondly, better technology. While I'm not sure technology is the sort-term answer, I do think that helmets will continue to get better and better. This probably isn't a solution in and of itself. What research I have read has indicated that at the end of the day, it's probably a bad idea to get hit on the head by a really strong dude running full speed - no matter what helmet is involved. Coupled with other techniques of increasing safety, though, technology has the potential to provide big dividends.
My final method of increasing player safety dovetails quite nicely with Dashon Goldson's hit on Early Doucet: the NFL ought to emphasize and insist upon proper tackling technique. I played football in high school (ladies...), and we ran tackling drills in order to emphasize proper technique - almost on a day basis. I'm not sure how redundant this would be at an NFL level. I would hope defensive players at least understand how to wrap-up and drive with their legs. Thus, it's a good thing that the NFL reviews and doles out punishment like that crappy candy the one neighbor always has on Halloween. Illegal hits cannot fly. They need to be punished.
With this in mind, though, the NFL should celebrate legal hits - like Goldson's. It allows the fans to continue being excited about football - a sport that finds its appeal in big hits and physical contact. It also allows other players an example of the type of technique they should emulate.