I just got Black Shark I'm currently having the same problem and it is quite frustrating.
I am patched 1.0.1
here's what I do:
start Para_Belleum's tutorial1.miz
win-home for 'cheat' start
wait for all systems to be up (i think)
i do not turn on or off any other systems or flip any switches... should i?
punch in waypoint 1.

use collective to take off to about 50m.
at this point I can approach 0 IAS and get stable(ish) but when I hit auto-hover nose pitches up and heli goes out of control.

alternately if I attempt forward flight, get to about 100kmh, -10 pitch, press trim, release trim, neutral my real joystick, then nose pitches up again and continues to go up.

in both cases my controls look neutral in the ctrl-enter red panel.

I do have a G25 and a saitek cyborg command unit also plugged into the machine, along with my x45.

Hope someone has some pointers!

(whoops, looks like it was the FF on the G25. turning it off solved it):
http://forums.eagle.ru/showpost.php?p=568722&postcount=15

With regards to initial posts.
I loaded up the sim and just tried to fly in instant (so was already in the air). I use the CH FS/PT/PP blah blah. Had to unassign all axis and reassign the exact ones to the exact device before the sim listened. Check none of your axis are double assigned.