How does a distributor with a b ig hole in the side effect emissions and would it make me run a rich fuel mixture? thanks

 

A hole in the cap or the distributor case? most caps already have vents to release the gas/particles from the sparks and an additional hole, depending how big may make little difference unless structurally. Caps are cheap so replace. If in the D case, a concern would be letting in the elements, water, dirt etc. as to not 'short' out any connections, corrode parts. etc.Find a way to plug it up.