Pulse Reading from Coin slot to Arduino

Gedon:
It doesn't count up continuously anymore, and counts up respectively to what coin is inserted. Still starting from 0 and not 1 would be a bit more of a convenience to me than finding a way to get rid of the unnecessary 1 on start.

From that page:

Something to be aware of is that these flags can be set before you attach the interrupt handler.

Before the attachInterrupt, try:

EIFR = _BV (INTF0);  // clear flag for interrupt 0
EIFR = _BV (INTF1);  // clear flag for interrupt 1