I tried using the demo code on an 8MHz pro mini board and had continuous problems with random lockups. I think there is a bug in the MPU6050_DMP.INO file.
There is a line with the comment
"otherwise, check for DMP ready interrupt"
and then
"else if (mpuIntStatus & 0x02)"
According to the invensense data sheet, the data ready interrupt is on bit 0 and bit 1 is undefined. Don't know if he was using some undocumented feature in in the MPU-6050 or if this was just a typo in the code, but changing the "else if" from 0x02 to 0x01 seemed to fix all my lockup problems.