Is my accelerometer precise enough?
Typically you can improve performance by analyzing the data that you want and analyzing the data that you don't want. I would assume that a plane can't turn infinitely fast so the actual "want" data is properly fairly band limited. Depending on how fast you are sampling the accelerometer you may pick up a lot of "out of bandwidth" noise. This could easily be improved with a low pass filter or some moving average contraption.  The more you know about the properties of the actual signal and the properties of the noise, the better you can separate the two.