As a US citizen what recourse do I have against a Canadian citizen who issued a cheque for renting a villa in Mexico then reported it lost or stolen to get out of the confirmed reservation contract after it was converted to US dollars & deposited in a US Bank, then reconverted and returned resulting in a loss of $82.51 plus a $15 returned check charge plus the rental fees loss?

I don't think there is very much you can do about recourse; as far as Canada is concerned, Mexico is a foreign country and the transactions alone would be hard to trace. Just don't arrange something like this next time and it won't happen again.

Almost nothing, you could turn it over to a collection agency.

If the check was "bad" I will assume you could file charges in Canada, I am not sure if they will let you do it by mail or not, but you could call up there and find out.