Sometimes I've thought that Saban's reputation for being a complete a-hole may affect the way refs call those subjective type calls on Bama. I've seen Saban yell at refs until his face turns Crimson red. I would think the human nature of refs makes them want to avoid those potential temper tantrums as much as possible. Football coaches are virtually never thrown out of games. They must be able to say some pretty awful stuff to refs, compared to baseball or basketball where it is common to throw the manager/coach out of a game.
I'd think it'd be the other way around. Most refs don't appreciate being shown-up, so I'd think they'd flag his team more frequently just for being a stupid prick all the time. I mean, really, what's he going to do? Even if it were possible that he'd try to attack them, he's like 5'2" and could really only bite their knees.
There should be a better review process of the calls made on the field. Maybe not in game but for sure after the game, and they should be held accountable for missing calls. Maybe not ticky tacky ones but anything blatant.
I think they are. I know that the coaches send in comments and questions on questionalble or contraversial calls. I think (not sure) that they get to voice any concerns weekly during the season.