The helicopters are working as they should.

Lifting off when the mouse is moved back and forth ... that's "as they should"?

If you mean that they usually do, yes, you're right, that's true.

When you move the mouse in any direction you are creating lift in the opposite direction. When you move the mouse in every direction, you create lift in every direction, as if just pressing Q.

1. Increase Collective is Shift. I don't know why you mention Q.
2. Moving the mouse changes the attitude of the rotors. It changes the orientation of the rotor plane, not individual rotor's angle i.e. not collective.
3. I'm talking ArmA3. Are you?

Of the many, many hours I've flown helo in A2, I have never ever seen this behaviour.
Of the many times I've gotten into helo in A3 (I use that situation as a rough benchmark while adjusting video, and for testing new OC) I have only twice (2 times) seen this happen.

I tried a number of times to make this happen again. It never did, except for this second time, quite by accident.

So you're saying that twice the helo responded properly, and all other times (where it required actual keyboard input to Increase Collective) it did not? That what I took as very acceptable and predictable behaviour was actually a failure mode?

FWIW I have never heard that mouse movement had any effect on Collective setting. Certainly not while motionless on the ground.

w/respect, I think you have a notion. but nothing more.

I've had choppers take off without pressing anything

BenTrem, I've tried to replicate your issue without success. Both with setting the helo down solidly (holding down collective and letting go) and also with setting down lightly (tapping down collective, stopping when contact with ground made.).

Observation 1: No amount of mouse movement in the menus had any effect on either cyclic, nor collective, nor antitorque when reentering the game.

Observation 2: Mouse movement in the game only had an effect on cyclic and antitorque and no abnormal lifting behavior was seen. If the landing was light, then the tendency would be for the aircraft to slip slightly across the ground.

Note: I fly with ArmA's default keyboard scheme. Using most current stable build.