So many great ideas brough up so far, any option I could cite as my "one thing I would change about the NFL" has been mentioned already. If I was "forced" to choose just one then it would almost certainly be the PI interpretation reform, since I think that one type of penalty is the biggest "X factor" in NFL football, especially in this pass-happy era.
I'm going to add in a few things here that may be of interest:
1. Change the way the Competition Committee is populated. I think this committee is too influential (OK, I know this is not provable, but I grew up in the "Shula Reign of Terror" and now we have to suffer from the "Polian Politburo"), and therefore provides certain teams with a competitive advantage. Obviously this is a vital committee, so there needs to be one, and it definitely would not be effective to have a representative of each team on it (keeping in mind that the rule changes are always subject to vote from the entire league), so the only solution is to staff the committee only with people that (A) have no current affiliation with any team, and (B) have relevant applicable experience, meaning they were players, coaches, football executives, and/or referees. I think all who serve the committee should be a couple of years removed from their affiliation with a team, and that noone should be able to go immediately from the committee to a team (perhaps a two-year exclusion period). I don't think anyone should be on the committee for more than a certain period of time, say 4 years. Finally I think there should be a mix of people (say 2 former players, 2 former officials, 2 former coaches, and 1 former executive).
2. Make the standards for league discipline less arbitrary and capricious. It is idiotic that someone can be fined $7,500 for spiking a ball but only $15,000 for concussing someone (through an illegal hit). Don't get me started on the whole camera on the sidelines instead of the coaches booth fiasco. There is too much "making it up as they go along" by the league office at this point, and like many people I don't think Goodell has any credibility in this regard. The system in place now is disfunctional, and it unfairly affects competition. The only solution that makes sense to me is to handle this like laws and regulations are done in "real life." Let the Competition committee determine the standards for discipline, done based on specific criteria. These standards would be approved by vote of league ownership, and the league office's role would be only to "police" enforcement of the standards. If some new issue arises during a year (for example, Harrison's recidivism) then that becomes a matter for the Competition committee to put in place for the following year (and not change the rules of the league during the year). Obviously if some crisis arises that requires more immediate action then this can always be done based on ownership approval.
3. Change the touchback rule on a fumble. I know this is very trivial, but for whatever reason it annoys me that if someone fumbles and it exits the field anywhere but through the end zone, the team retains possession, but does not if the fumble goes through the end zone (if the fumble goes through your own end zone, its a safety, but if it goes through the opponents end zone, the opposing team gets it at their 20). I'm OK with the safety for fumbling it through your own end zone, I wouldn't change that, but for the rest of it, it would make more sense to me if the rule were simply that when a fumble is not recovered within the field of play, the team retains possession from the spot of the fumble.
