Power supply issues with many identical PCBs
I am surprised that this would work at all. There are open GND and (A)VCC pins that are required to be connected for the MCU to work correctly.

Atmel has an appnote how to wire the power lines on their chips,
you need 100nF for each VCC/GND pair close to the pins. AREF should be wired to an 100nF capacitor with its other pin connected to GND.