Arduino Based Digital Level Code Review - How does it work? 

No issues at all. Have you tested with a different library to see if you still have issues? If so could be your wiring or hardware related.

@@DesignBuildDestroy I will try. I have noticed that you have not used the interrupt pin,but for DMP to work interrupt pin is needed? as per documentation. Pls comment

Not sure, but throw some Serial.Println's around the calibration lines and see where it actually hangs up to troubleshoot. There really isn't anything in the code that would make it stall unless the MPU board itself is locking up

@@DesignBuildDestroy Sure I'll try that. On the serial monitor for the moment only a long series of "*" characters are observed. Looking at Rowberg's library code, there's a Serial.write('*') every time the data are not good for calibration; a comment says "Error is still to great to continue"; typo on "to" included in the original comment :) [function `PID` in MPU6050.cpp]

Kinda defeats the purpose but sure.