I think the biggest impact of dropping AoOs is in character advancement, specifically with respect to a couple of skills, several feats, prestige classes, and spellcasting. Tumble is rendered useless, as are Combat Casting, Combat Reflexes, Mobility, and Spring Attack. There are feat chains that start with those feats, and the upper ones are suddenly much more expensive because you have to buy totally useless feats to get to them. The same happens to prestige classes. Further, some class abilities become pointless, like the duelist's improved mobility. Dervishes and scouts have nothing to prevent them from doing their little dances of ruin.
Other things that are affected: all the special combat options are more likely to happen because they no longer provoke AoOs, while their corresponding feats are simultaneously decreased in value. The squishy mage is going to be a much more attractive target for monsters to attack because there's nothing the tank can do to stop the monster from getting there.
That being said, the game runs relatively smoothly without AoOs. It's just that there are long term effects that make it harder for players to understand what changes in the relative value of their PC choices.
-blarg