My recommendation is to limit weapons to sidearms only when shooting from the passenger seat. Seems the best way to handle it, and in a "real world" application (snicker) it seems the most likely to happen.

Create a new turret placement for infantry to use their own weapons. Only 2 players would be able to do it per dropship and the ship would be sacrificing its small turrets to do so. Most weapons would be useless because the height that dropships have to fly at in order to avoid being demolished would put them beyond reasonable range. Mass drivers would be great but you'd have to fly about 25m off the ground and keep it steady for them to actually hit anyone on the ground because the rounds expire after a few seconds.

The biggest issue would be forge guns and swarms taking out tanks from the sky - this could be averted by simply making the swarms and forge blast hit the dropship itself because you really shouldn't be firing something that powerful from a paper plane.

I think it's about having to hold on while flying around. I think while flying you can shoot sidearms and non shoulder mounted light weapons form the hip. If the DS is stable you can crouch (better balance) and fire anything with aim down sights. Too much speed/acceleration and you stand up instantly loosing lock-on for swarms and charge on FG.

Ah, but heres another question. Is it really acceptable for gunners to shoot out of a dropship with shields? Wouldn't their weapons just hit the shields?

these guys are clearly shooting out of a helicopter with LMGs, and ARs...

http://www.youtube.com/watch?v=b7O7ovNi42U

in modern ware, and modern warefare 2, and modern warefare 3, there were several spots in the story mode where you could shoot from helicopters... and of course enemies could shoot oyu back. for example:
http://www.youtube.com/watch?v=u9kYtesQkVI
go to 1:58 second marker and see what he does

http://www.youtube.com/watch?v=Mij3IwTghHg
notice 12:51 and beyond

ooppss... they didn't.

The shields don't cover the passenger bay. You can shoot right through the middle of a dropship with its doors open.

I sense sarcasm.

Wrong vehicles dont catch fire if the incoming damage is greater then the total amount of HP left remaining. The only time where vehicles in dust catch fire is when they survived a critical blow with like less then 200HP left remaining on armor. When they burn they can survive for like 3 secs on 0HP but at that point a militia AR can finish them off.
Example on how it works currently:
-LAV gets 1 shoted by a forgegun with no chance of bailing from the vehicle
-Dropship gets aswell "1 shoted" but it doesnt explode the engine just simply fails while the vehicle itself is still intact. The finishing blow in this case is then when the dropship hits the ground.
So you see the dropship crew has like 2 secs to bail from the vehicle while tanks and lavs explode instantly with no "bail timer".