I don't have any calibration issues with my G940 but the auto pilot problem is because it doesn't have a centering spring action. The slop in the center makes it difficult to have the stick centered well enough to keep in in range of auto pilot operation. Unfortunately there is no way to adjust how much the stick can move before it turns off auto pilot in Aces High so you're stuck with this problem.
That used to annoy the heck out of me when I first got it but now I've gotten used to it.. it's just a matter of balancing the stick in just the right position and looking one last time as you walk out of the room to get a beverage to make sure you aren't pointing nose down into the ground...
When you calibrate it make sure you actually have the stick centered (and not just let go of it) otherwise it will calibrate the wrong position as being center.
Also make sure you have the newest firmware installed (Located
HERE) as it almost completely removes the hysteresis (also known as the reversal bug) from the stick's X/Y however this will still happen in all other axes (including trims, rudder, throttles, etc). If you don't know what I'm talking about refer to this demonstration video:
http://www.youtube.com/watch?v=SZlUWwOJUN0If/when (with emphasis on the WHEN) you start seeing spiking issues in the throttle plan on rewiring the throttle. It starts out with the throttle trims dropping out as you move the throttle and eventually makes buttons quit working, etc. Its wiring is a little to fine and the harness is a little too short and they all tend to break.
Also if your rudders spike you can replace its pot with a quality CH pot. It's a pretty easy replacement.
If the hysteresis becomes too annoying you can always rewire your stick and rudders through a third party controller (I used a Bodnar BU0836 board). The hysteresis is a failed attempt by Logitech's engineers put in place at the firmware level to help to compensate for gradual wear and jitter/flicker from the pots. Unfortunately they failed miserably and accuracy takes a huge hit in the process. If you want to see more details about my modification feel free to read about it
HERE.
I will warn you this stick is really neat but has a lot of well known problems and Logitech quit supporting and developing it completely. After they released the final firmware almost a year ago to this day no updates have been released and no one will talk about it. It's kind of like they just want it to go away. They'll still honor the warranty and replace your unit with another flawed product but don't expect anything else from them.
While I love mine unless you want a project my advice is to return it for a refund if you can and run away... as fast as you can! If you want to play around with it some then it can become a very nice stick.