There are a handful of bugs with the helicopter that I hope to god get fixed. I fly with the Xbox controller and made a video proving the pitch and roll commands stop responding while descending: http://www.youtube.com/watch?v=TcKu42-ASEk
Also, whenever I would descend (left trigger) the freelook would enable, after opening up the BF4 Settings Editor I found there were 2 "Freelook(hold)" : http://i.imgur.com/P0X0yaA.png I heard there were some problems with the tanks and their zoom similar to this.
It seems some of the keybinds are "hardlocked" in the game. I even tried to disable the xbox controller all together and edit the controls with the keyboard, but the game was still picking up commands from the controller.
Edit: Just did a little look around and I think its because the hidden freelook button is set to my left trigger. Even though I turned it off its still thinks freelook is on thus not letting you control the helicopter, just crack it open with the battlefield 4 settings editor and check both the freelooks with the same command http://battlefield.realmware.co.uk/bf4-settings-editor/downloads when launching the game it will ask for local or cloud saved data, both of these will rebork the controls, to fix this, open up origin, click the origin tab, scroll down and uncheck the cloud storage, and everything should work a lot better. although, every other time i die the freelook wont work, but the controls should still work fine. (there shouldn't be this many hoops for something as simple as allowing personal keybinds)