I favor Bullwinkle’s rendition (as a waiter, serving Boris Badenov):
Oh, the taters are old and the meat is a fright
Everything is left over from Saturday night
We sweep it all up, throw it into a pot
And we say that it’s real Irish stew that we’ve got.
Thanks. I asked two different people in real life at various times and they both tried to tell me it was the same tune as the Mexican Hat Dance. I just don’t see it personally. Or maybe my sound reproduction isn’t as good as I’d like to think.
There’s another really common stereotypical Irish tune that I’m wondering whether it’s actually a tune or just a motif. I alas can’t think of an example of it right now. It’s a much simpler little riff.