Even if we are only dealing with words (unlike, e.g., `sacrilegious') which contain each vowel only once, and in alphabetical order, `facetious' is not the only such word. Ignoring the obvious `facetiously', which has the six English vowels in alphabetical order1, there is `abstemious' (and `abstemiously')--which, interestingly, is a near-opposite of `facetious' in meaning.

  1. Some people might consider syllabic n, m, and l to be vowels. Others might consider the `w' in `row' to be a vowel, but it is more of a glide or semivowel. Depending on what dialect you speak, final `r' might be a vowel, might be a semivowel, might be a trill or flap, or might be silent. Additionally, in some languages using the Latin alphabet, `w' or `r' are vowels (`w' in Welsh, `r' in, for example, Serbian), and there are many vowels with diacriticals.