Physics; NPCs and enemies walking through vehicles and other objects. NPCs walking through vehicles, then getting stuck and causing the vehicle to violently backflip. NPCs, and enemies even during the middle of a fight, walking through vehicles and becoming stuck beneath them somehow. NPCs tripping over an object and then becoming permanently intert. NPCs remaining alive while a vehicle is firmly planted on top of them. When firing a rocket, or tossing a grenade, at a vehicle while you are outside it's field of vision - it will not respond at all. You can barrage it with explosives until it is destroyed and it won't so much as rock. Only once the vehicle has entered the panic state will it react physically.
Spawning; Vehicles, though much less frequent than at launch, spawning below my vehicle and causing me to be shot into the atmosphere. My vehicle spawning beneath, or inside of, another vehicle and causing them to both explode. An entire crowd spawning into one another at specific locations. NPCs spawning half-way through walls and objects, spawning on chairs that don't exist, etc.
AI; NPCs, and even enemies, will not respond to grenades or rockets exploding if you remain in cover and no one has been injured or killed. You could fire rockets throughout downtown and/or, as I did accidentally, toss a grenade from stealth during a mission and none will be the wiser is no harm was done. The city traffic comes to a complete halt if you, a vehicle, your vehicle, or another person stop in the middle of the road. Police not responding to being shot by hostile NPCs. Really, that last one still gets me.