I'm not convinced that it's not a grammatical mistake.
The thing is that the line was something he came up with once they'd landed. In other words, he was reciting a line, not generating spontaneous speech. If an actor forgets a word, it's an error in memory, not in grammar. Also, Armstrong has apparently admitted that he sometimes drops syllables in speech, which means it's an error in speech production, not in grammar. Either way, it's not a grammatical error.
What bugged me about the article, though, was the way they portrayed the error. They said that "one small step for a man" is "more dramatic and grammatically correct." I don't see how drama factors in at all, and if the "one small step for man" version is incorrect, then it's not an issue of one version being
more correct. Correctness in this instance would be a binary thing, but they seem to be portraying one as proper an the other as improper. I don't think that accurately describes the situation.
Edit: On a related note, Language Log has done a couple of
interesting posts on the subject. Far more interesting than the virtually content-free CNN article I linked to, anyway.