Let me see if I understand you all correctly:

résumé is incorrect because it (1) does not represent the way we pronounce the word in America, and (2) is pretentious to certain people.

resumé is incorrect because it (1) is not the way the word is spelled in French, (2) has an accent, something true English words do not have, and (3) therefore is the worst option to some people because it is neither an English word nor a French word

resume is incorrect because it (1) does not represent the way we pronounce the word in America, (2) represents the epitome of American laziness to certain people by demonstrating a complete lack of effort to find a way to type accents, and (3) does not distinguish itself from another English word.

Funny.

Personally, I feel that if all of the spellings are in the dictionary, they're all right. But on style preference:

I don't like "résumé" because it's not the way we pronounce the word. If you're going to put accents on a word, you should pronounce it like the accents dictate. To do differently demonstrates, to me, thinking that you're smarter than you are... in other words, pretentiousness. In my view, you're either French, and you spell it résumé and pronounce it exactly as the French would, or you're not French, and should leave that spelling (and pronunciation) alone.

I can also see others' points about "resumé" not making sense because it is neither the "correct" French spelling nor a "correct" English spelling. Despite seeing their point, I believe "resume" is a worse option because it does not represent the proper pronunciation, and, to wit, we never pronounce an "e" at the end of a word like that without putting an accent on it. Resumé is also an accepted spelling in dictionaries, so those passing judgment on it because it is neither "proper" French nor "proper" English appear to me both wrong and, again, pretentious. It is obviously a proper English word, or else it wouldn't be in the dictionary (or would at least have informal, slang, colloquial, or some such designation next to it). The arguments stating otherwise are specious.

When it comes down to it, it appears that the true problem is in our pronunciation. We should have either kept the original French pronunciation or dropped the accents altogether. Instead, we've kept a hybrid of English and French for our pronunciation (which, to me, lends credence to the idea of using a hybrid for the spelling, as well. Just think about it--what's the point in pronouncing it as a hybrid and then spelling it with the original French accents or with "proper" English convention. We say it as a hybrid, so spell it as a hybrid!).

That being said, the thought of my é getting converted to an i or any other character scares me, so, because "resume" is also an accepted dictionary spelling, I will likely use it for all of my business contacts.