Throughout the course of any NFL game, it's really hard for the refs to be perfect on every play. There's not enough of them to see every player matchup every second to get every call correct.
I know we all like to think it's easy to get every call right because we're staring at a TV screen with a broader angle, and then we see the replays. But if any of us were refs, we damn sure wouldn't be perfect either standing on the field and trying to keep up with players who are moving all over the field.
So, the NFL needs more refs who are watching from different angles and watching different matchups, and these can be "remote" refs sitting in a studio (or even at home). And they should be able to make their own calls (or can reverse other calls & pick up flags). So for every NFL game, you may need like 4 to 8 more remote refs who can seamlessly buzz into the Crew Chief at a moment's notice. And for the playoffs, have even more refs, more eyes in the sky, to try to get each play right.
And make every flag reviewable, letting the coach challenge whatever they want.
Certainly all of the above will slow down the games, but I think as players and fans, we'd rather they get it right in realtime (even if it requires more stoppages), as opposed to having the game end 15 to 30 minutes sooner.
With all the technology we have available, it's time for a change...especially in the playoffs.