Penalty Challenges
When the NFL instituted instant replay, it didn’t work as planned, and they eliminated it, tinkered with the rules, and finally brought it back. Under the current rules, each team gets one challenge a half, and if successful, the refs overturn the play, and if not, they lose a time-out. Replays have worked well when going to this format.
Expanding upon the challenge rules, the NFL could add something similar for blown penalties. With the replay challenges in place, give each team one penalty challenge a half. The referee’s review to see if a penalty occurred or not, and the successful team gets the play overturned to their benefit. If they lose the challenge, they could lose a time out as with normal replay challenges, or perhaps if they lose the challenge, they lose five or ten yards. That adds an extra layer of strategy and keeps the coaches from challenging the more minor penalties in favor of ones that would have a larger impact.
Again it’s not a perfect solution as the sky judge might be, as the referees can blow a large number of penalty calls in a game, and the teams are just limited to one challenge a half, it’s a partial solution at least which address the issue of blown calls.
None of these solutions a by far perfect; however, each has its own merits. Plus that’s not to say someone could not suggest a better idea or they could at least try emulating the NHL and have something only for major penalties.