I had this same problem, both on takeoff, and in flight. In fact it was almost a deal-breaker - thanks to the forums I worked out what my problem was (YMMV).
Firstly - deadzone - this has been mentioned. My rubbish wireless joystick needs a deadzone of 4 on all axes - this prevents constant uncommanded (well, kind of!) yaw and sideslip. The other problem seems to have been the AP heading hold channel ("HDG" blue pushlight I think it is). If I'm navigating a route, I leave all channels on and Flight Director off. If I'm manually flying, I kill the heading hold and sometimes the altitude hold as well. If I want to do funky maneouvres, I hit the Flight Director on.
Then there's trimming. Contrary to what most have said, I don't get on with either press-and-hold, or single-click-when stabilised. I find that I do best when I make a turn (or whatever), stabilise, and then make multiple clicks of the trimmer button (note that the KA-50 cockpit video on youtube seems to show the pilot doing the same thing - I could be wrong though). It seems to prevent cockups - I can't seem to get the "click and release stick within 0.5 seconds thing" down - this bypasses it. And if I get way out of shape, I have trim reset mapped to the button right next to it - saves my noob skin often at this point.
The above has got me taking off smoothly, flying without porpoising all over the sky, and performing vertical landings - I can even translate across over the runway before landing, Sea Harrier-style. A week ago I couldn't do any of that.
This may help, or it might not. I hope it does! I for one am hooked on this thing.
