Electricity Energy/Power measure with Different power factor
Then these two signals go to ADC inputs of microcontroller PIC18F46K80
  to be multiplied and get the power


It is unlikely that simultaneous sampling will be used so there will inherently be a phase error of one sample period.


  The problem is when the phase change between current and voltage, the
  energy measurement error changed by 0.8% if the power factor of
  measured energy changed from 1 to 0.8L.


Yes, that sounds like the problem of not sampling simultaneously - close to unity PF the error due to this will be small and, as the phase angle gets bigger (lower PF) the error will increase.