[The following story is completely true, with no embellishment whatsoever.]
Recently I was in the waiting room of a doctor's office and a white-haired, elderly man came in accompanied by someone who didn't stick around. As they came in the companion asked him if he remembered the doctor's office. As he hobbled over to a seat behind me he replied in a genial tone that he did.
As I sat and filled out the paperwork on a clipboard (requisite for the first visit to any medical professional) I heard him chuckle as he read one of the magazines he'd picked up from the waiting room; I don't know which magazine it was, but he chuckled at it several more times so clearly it struck his sense of humor repeatedly.
At one point I heard him get up and amble over to the counter behind which was one of the ladies of the staff engaged in whatever activities occupied her time. He asked her if she wanted to hear a joke, and she replied "Sure."
"What do you call an elephant combined with and a rhino?" he started.
"I don't know—what do you call an elephant combined with and a rhino?" she said, making that clear effort to repeat the setup question.
"Elephino." Although I couldn't see him, I imagined him doing his best to shrug to play up the way the hybrid of the animal names sounded like saying "Hell if I know." The woman laughed in a way that seemed to be at least partially genuine and not entirely patronizing.
Emboldened with that success, the man rattled off a couple more such riddles, both of which elicited chuckles that grew a bit more patronizing than genuine.
Undaunted, he proceeded with yet another. "How do you get a one-armed Polack out of a tree?"
I detected a moment of trepidation by the woman upon hearing that setup, but the man remained oblivious to that. "Wave," he remarked with the same delight he'd presented each of the preceding punchlines.
"I like the 'elephino' one the best," the woman noted in a clear ploy to indicate the festivities needed to conclude. The man sat back down.
Shortly thereafter another patient entered and I'm not sure whether he knew her or not but it sounded like they were familiar in some way. He bombarded her with a number of different jokes, including: "Do you want to see my Harpo Marx imitation?" and then silence. (Go look it up, kids.)
She remarked at one point about how amazing it was that he could remember all of them. The only joke I noticed him repeat was the about the one-armed individual, which went over about as well as it did the first time.
Although he had a good memory for these jokes he'd learned, he had not gleaned the lesson one needs to learn when it comes to telling jokes.
You may be thinking that I'm implying the lesson is that he should have figured out that in 2010 jokes based on a stereotype of Polish stupidity is not only hideously outdated and would be likely to elicit an uncomfortable reaction from those who recognize its inherent bigotry. And while all that's true, that's not the lesson in question.
Certainly the joke exhibits insensitivity, but the awareness of something being insensitive is not something one would just figure out (especially when one is oblivious to patronizing laughter); one would need to be told outright, and clearly that's not going to happen. And heck, for all I know the man was operating on some hyper-ironic level where he secretly intended to test the boundaries of good taste (a la Sarah Silverman); comedy can operate on many different levels, and offense is ultimately something the listener chooses to take, not necessarily a universal construct. (I'm not here to pass judgment. At least at the moment.)
No, the lesson is this: When telling jokes (unless you are on a stage with a microphone and an audience who is expecting you to entertain them) always stop before your audience makes you stop. If one joke is appreciated, it doesn't work out that seven jokes will be appreciated seven times as much (whether you have an archaic risible joke in your repertoire or not).
Leave 'em wanting more is a comedy adage for a reason.
The joke in question fails not so much because the era when putting down the Poles was en vogue (although that would have some overlap with the time when people in general grasped that the Harpo Marx character never spoke) but because it blithely overlooks the key aspect of the suggested situation. If a one-armed person of any nationality is adept enough to have gotten up in a tree in the first place, it stands to reason the he could hold on to a branch with his legs and leave his arm free to return the greeting.
One need not resort to political correctness when one has glib over-analysis. (Perhaps a comedy credo in the future?)