I just want to know what will happens if decoupling capacitor across supply pins is not used for PIC Microcontroller
What kind of problem we can face ?
Generally speaking un-bypassed supply pins generates lots of clock jitter, and you can have
the processor fail to execute code and other HW properly. Datasheets have bypass recommendations.
Strongly suggest you adhere to them.
For a circuit one of the most important things is a stable power supply.
Instructions may not properly processed, ADC may not work properly, Reset/brown_out may restart the processor....
Everything relies in power supply, thus everything may fail.