I think the position of the authorities on mistakes made by the referee undermines them and loses them respect. Let the referees admit mistakes and reverse decisions after the match. This insistence on not reversing decisions because the referee "saw" the incident (when he obviously didn't see the key part) just makes him look bad. Infallibility should be left to the pope. Let the referees be human and admit mistakes.
Then help them on the field. Some form of video review is a no-brainer. It's stupid say no technology can correct 100% of the mistakes so we will keep all the mistakes. If technology can reduce 50% or 90% of the mistakes the game will be better.
I think rugby has some good ideas that help respect for the referee. If a player pushes the referee, he is gone, no questions asked (as in the NFL or NBA). Only allow the captain to question the referee, then he can shoo the mob away and take action if they don't. The reversal of penalty decisions and moving the ball 10 yards/metres work well in rugby. If a team gets a free kick outside the area and their players start question the cards given, then give the free kick to the other side. They lose the goalscoring opportunity. Similarly with corners, reverse it to a goal kick. Managers would soon tell players to stop complaining, especially if they lost a penalty. Moving the position of the free kick isn't such a clear advantage in football, but would help when the kick is 30-40 yards out. For close free kicks, 20-25yds, perhaps the ref could move the wall further back if the defenders complain. Give the ref an array of sanctions like these and players will be more careful.
As already mentioned, the appeal system works well in many sports and overcomes the disrupting continuity argument. In truth we lose enough time when the referee is dealing with scuffling players at corners and free kicks, so if the players show more respect when told what to do then we could gain time that can be used for reviews.