Uh, yes they do. And when the lag gets bad, you'll see major delays between when you order a unit somewhere and when it actually acknowledges it. There's no need to network your actual mouse cursor itself, so it's not affected by latency. In an FPS, your reticule is your 'cursor' and is where your player is actually pointing towards in the simulation, so it needs to be networked. I just brought that up as an aside though.
Heh, beat me to the punch.
In FPS games, the camera angle must be synchronized for all clients.
In RTS games it would only be used for anti-cheat measures by the host, to verify an input is valid.
CoD's network AI is not substantial nor has to deal with the complexities or amount of AI that Halo does. Actually count the active AI you see in one scene in the game without triggering a new encounter. Rewatching campaign CoD encounters, I never can seem to count above 5-6. Now go play Reach and notice how many AI are present in a single continous encounter, loaded up at once, or how many will be spawned in at one time in Firefight. Looking at video real quick (I can't get on the Xbox right now), the wraith encounter on Pillar of autumn (right after the mongoose jump) has around 25 active AI at once.
As you said earlier, the AI doesn't matter for networking, that is the whole point of using the networking model they do.
The thing that COD does to help networking is limit the amount of entities that need to be networked.
All of the enemies in Halo shoot projectile weapons. Almost all of the weapons used in COD are hitscan, besides launchers and thrown equipment.
Plus, all of the Infinity Ward games only have two player co-op max. Treyarch does four person zombies.