Google Sky Maps does not follow pointing direction. How can the sensors be calibrated? I have a new Lollipop device (Moto G 2. Gen) and wanted to use Google Skymaps. This worked like a charm on my old device. Now the display is not following the movements of the phone in the right way.

I think this is due to missing sensor calibration. I am missing a corresponding item in the Sky Map menues and I neither could find it in the general settings. How can i calibrate compass and accelerometer on my Lollipop device?
I guess you mean to physically wave the phone in a pattern of a three dimensional infinity symbol (or simply a figure of 8).  This YouTube video gives a good demo.

Moto G2 has gyro in addition to what Moto G1 have. Hence it should work like a charm and the issue you are facing should be a calibration issue at a low level.