The PIC12F675 has two Vref options.
VDD is Vref. or Pin "GP1" is Vref
If VDD is Vref then your +5V needs to be better. A Zener is not the best regulator.
-You could change the Zener diodes to 8.1V to 12V and then use a low current 5 volt regulator to give you a real good +5V.
-You could use a TL431 on the GP1 pin to make a real good 2.5V ref. (then the 5V could vary) (TL431 needs 1mA of current)
VDD is Vref. or Pin "GP1" is Vref
If VDD is Vref then your +5V needs to be better. A Zener is not the best regulator.
-You could change the Zener diodes to 8.1V to 12V and then use a low current 5 volt regulator to give you a real good +5V.
-You could use a TL431 on the GP1 pin to make a real good 2.5V ref. (then the 5V could vary) (TL431 needs 1mA of current)