If i recall correctly, they did remove the football move rule. To be fair the spirit behind the rule was to differentiate between a fumble and a incompletion, not between a catch and a not catch.1) Define a catch as two feet, a knee, or your butt plus possession. Dump anything after that in the current description (maintaining possession through hitting the ground, making a football move, etc.)
2) Spell out in the league rule book, operations manual, CBA, etc. EXACTLY what is allowed and not allowed within the rules and what the penalties are. Then enforce it, no exceptions or mitigating circumstances. First time offense for domestic abuse means 6 games. a 4-game drug or PED suspension needs to be 4 games. Also, leave the marijuana policies on the books but just don't test for it. Save that for guys with other issues that you can't nail them on and then hit them with a pot suspension if all else fails. This would limit the power of the commish to make up suspensions and would get the players to stop appealing and whining about suspensions, The NFL needs consistency.
3) For egregious, targeting, or blatantly cheap shots, the person committing the foul is suspended for as long as the injured player remains out. If the player does not miss time, have a progressive suspension system (1 game the first time, 2 games the next time, 4 games the third time, 8 times the fourth, etc.). So for this one, the party with the cheap shot would be out for whichever were longer (the amount the injured player was out or the progressive suspension).
4) Take away the automatic first down component of defensive penalties. Nothing worse than seeing a 3rd and 38 become a first down for a ticky tack 5 yard defensive holding penalty on an 8 yard pass. And while we're at it, eliminate defensive pass interference on balls that are clearly way under thrown. Offenses should not benefit from a bad pass which many times is the QB just trying to avoid a sack. Also need to better define and call offensive pass interference on rub routes or bubble screens. I have seen the same type of play in the same game called OPI, not called at all, and defensive holding.
5) Make all aspects of all plays reviewable and each team gets 3 per game, but instead of losing a time out, if you lose a challenge make it a 15 yard penalty. That would cut down on stupid challenges, especially if winning the challenge wouldn't even net 15 yards.