Trivet, funny video! :-) I'd always heard it had to do with whether the article "ein" was used before the word. On the other hand, why it should become such a legend when Jimmy Carter's mistranslated "carnal lust" episode hasn't is beyond me. ;-)
I agree that "ich bin ein Berliner" has attained legendary status. Occasionally the History Channel (aka the Hitlery Channel) or the Discovery Channel will run a program about the history of Berlin from 1945 onwards, always including the clip of that JFK speech - it remains extraordinarily moving, even after repeated viewing. And Berliners still retain a huge amount of residual good will towards Americans to a degree that would be hard to find anywhere else in Europe.
I have a particular soft spot for the city and its people, having worked there every summer while I was in college and studied there for a year, living just two blocks from the Wall. The only book of Leon Uris that I ever found even halfway palatable was the one about the Berlin airlift - generally I found his insistence on couching all his stories in crudely broad-brush, good guy/bad guy terms irritating and reductive. In the case of the Berlin airlift it didn't seem completely inappropriate though.
I tried this on a few people when I lived in the former East Germany and generally they opined that Kennedy had not said he was a jelly doughnut. The video footage of the speech appears to bear this out as the crowd do not roll about laughing when he says it. Not like I did when I first heard it :-) In any case, the fact that there's a reasonable amount of interest in what he implied - we know what he said - so many years later means that it has attained legendary status.
Unfortunately there have been a few Presidents since then who really were jelly doughnuts and did not have the grace to admit it.
Well, sometimes Wikipedia is even more annoying than Weirdnet. when I lived in Berlin, all of my German friends agreed that Kennedy's inclusion of the indefinite article was incorrect, albeit unimportant.
Also, I'm not sure I would classify this as an urban legend - there is no dispute about what he actually said.
Regional and temporal variation in The naming of baked goods is an issue I'm not going to touch with a ten-foot pole. In 1974, in Westphalia, "Berliner" did mean jelly doughnut, but by now the meaning could have morphed to "a snail-shaped contraceptive device to be used by men".