It doesn't matter one bit what her name was "supposed to be" if they released it as "Aeris." I don't care if it was a mistake or not. A mistranslation, a snafu, a late-night drunken joke, none of that matters.
"Aerith," when used in the west, is usually a sign of elitist hipsterism, and quite silly.
When "Aerith" is insisted upon, it's just hipsterical.
For the one, the transliteration "Aeris" showed up in not one, but TWO Final Fantasy games (Tactics is the other).
For the two, 's' and 'th' are both transliterated into Japanese by the same symbol (pronounced 'su') which is the last syllable of Aeris's Japanese name (Earisu), and it's always been that way from the beginning.
For the three, "Aerith" sounds moronic, whereas "Aeris" sounds...less moronic.
For the four, "Aerith" only gained traction in the west when someone decided "Aerith" was almost an anagram of "Earth." Which, of course, is a bloody coincidence, and points to this 's' vs. 'th' junk being ex post facto revisionist gobbledygook.
Look, it boils down to the fact that the majority of us spent AT LEAST 7 years calling her Aeris, and there's no substantial reason at all to go back and change that now. I still have my copy of FFVII from 1997, and it still says Aeris. My Tactics still says Aeris. I still say Aeris.
Also, I want to point out that there seems to be an incorrect understanding of how "canon" works perpetuating in this thread. Canon is about a body of work. You can't cherry pick elements of a work of fiction. You can cherry pick works of fiction, but not elements within individual works. Do you follow? In other words, if you want to say that "Aeris" isn't canon, then you have to say that FFVII the game as published in the west isn't canon. The whole game. For me, FFVII is the most canon (only canon?), and the other games/movies/whatever are the deviations. Fun/interesting deviations, but deviations nonetheless. Nomura doesn't give a rat's rear end about continuity. Neither does Kitase.
Now, if SE ever gives us a FFVII remake (would make sense as a 20-year anniversary gift to the fans, yeah?), and "Aeris" is changed to "Aerith" then I'll consider the canon officially altered (though I myself will still call her Aeris--for the most part).