Interrupts are firing when touching ground with metallic things
People typically regard the internal pull-up resistor of the AVR reset pin as being slightly weak. I would consider putting a pull-up resistor of 4k7 on there as well as a capacitor of say 100nF or so as breadboards typically are noisy environments.

With noisy I mean that the connections on the breadboard can be a higher resistance than expected due to oxidation of the connections, glue on component legs from reels or general muck. This can makes the design more vulnerable to external influences.

When your design has a higher resistance than expected you can run into weird behaviors such as the one you have encountered now; by touching the ground wire you are transferring some of your charge to the circuit. This will change the voltage your circuit sees from the IO pins with regard to the ground plane.

Possible fixes are;


Clean up component legs with some acetone or alcohol to prevent bad connections
All ground and positive power supply connections should always go to or from the power rails on your breadboard; do not hop from ground pin to ground pin with jumper wires.
Consider a higher quality breadboard as there are some low tier breadboards out there that will make your life difficult. Low quality breadboards are plagued with corroded / bad contacts.


I should also mention that it is typically considered a bad idea to work on electronics without some ESD protection; the charge you accumulate can be enough to cause a permanent malfunction of the electronics you are working with. Admittedly AVRs are tough beasts and can take some abuse but you should still take some precautions like an ESD wristband and an ESD mat if you haven't already.