I know the difference between HAshi and haSHI (and 'haSHI GA', for that matter,) but how important is some level of skill with pitch accent? Will I be totally misunderstood, or just easily identified as a gaijin (assuming I'm talking over a phone or intercom?)
Hard to say. Probably not all that important, although there are anecdotes about people from one part of the country being misunderstood in amusing ways in another part of the country. Certainly in Tokyo, native Japanese from all over the country manage to get along without changing their accent. One would suppose that just about everything would be expected, let alone tolerated, from people who don't look like they might be native Japanese.
On the other hand, I have been corrected over and over again during my attempts to speak Japanese, and not only by my wife (who is often wrong, anyway). Sometimes it's because I was misunderstood, like once I called a kettle a turtle (ka|me instead of kame|) in a context where "turtle" might have almost made sense (as is pretty well known in this NG, my Japanese is of the sort that "almost makes sense" anyway). Sometimes it was just because a cranky person wanted to complain, I think.
Meikai Nihongo Akusento Jiten (明解日本語アクセント辞典) - a pitch accent pronouncing dictionary.
"日本語発音アクセント辞典" published by NHK.
Part of this answer was edited from posts by Bart Mathias.
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