Lol - no, I did not hear much about the MAD magazine, but in England, it was popular, except for certain satirized people, like the Royal family, for instance. And no, I did not know this expression. But I am ready to learn further ...
So, I had to look up slang vocabulary and check, as in this case, the word "crackers" seems to stand for "crazy" (insane) or "mad", "rozzer" for "police officer", dropsy (not likely to be an oedema), rather for "tip" or "bribe", "snide" most certainly for "fake" or "counterfeit" (besides derogatory, mocky or an unpleasant person) - and I deepened into more info about MAD, Margery Allingham and the novel, referred to by the infos on the MAD magazine:
I think that the links answer the question, but they invite to read more about it.