Specifically I'm curious about the law in Longmeadow, Massachusetts prohibiting two men from carrying a bath tub on the town green., and the law in Boston allowing for a duel at a certain time of day on the green
I've spent more than a few minutes poking around Longmeadow's bylaws and regulations and I don't believe there is such a law.
Often when you see wacky law compilations, they apply a general, reasonable law to an absurd situation. For example, you need a special permit to own an elephant in South Carolina--the wacky version is, "In Possum Kingdom, SC, you need a special permit to keep an elephant on land where evergreens grow." It's true!
Best guess is that the park regulation against trash and debris is the general rule.
Also, if you know anyone who works for the town, ask them to get rid of that damned surplus apostrophe in the menu.