"in every respect" vs "in every aspect"

I can't see (or hear) anything wrong with:

Every aspect of a translation shall be excellent: its style, formatting, words, and meaning.

Here, the 'feature' sense of aspect is being used.

So I don't see how one can argue on semantic grounds that the following is wrong:

A translation shall be excellent in (its) every aspect: style, formatting, words, and meaning.

Syntactically, it seems fine too.

Which only leaves us with concerns about style.

And I'd agree that the second alternative here sounds decidedly unnatural - and I'd also agree with Barrie that it's because '[t]he usual collocations are in every respect, but from every aspect ('from' referencing the transferred literal, viewpoint, sense of aspect - from every aspect, transference of from every viewpoint). The first offering here avoids the unusual prepositional usage by avoiding use of the preposition.

Respect here has the meaning ‘a particular, a point, a detail’. Aspect would not be appropriate. It means, among many other things, ‘the appearance presented by an object to the eye’.

The definitions you are using for aspect are subtly different from what we are talking about. Very often, a slight shade of meaning makes a big difference to how we understand something. Unless you grasp the slight variance in meaning, you won't grasp the usages in question. Let me explain by using a single example. You point out that one meaning of "aspect" includes the word "character." When I read your comments closely, it appears to me that you are confusing this meaning with "characteristic," which is what "style, formatting," and so on, actually are. They are characteristics of the work, whereas "character" is the overall defining substance of something. The other two words in this definition, "nature" and "quality," are meant here to mean exactly that: the entire identifiable "thingness" of whatever you are talking about.

If we then take this meaning of "aspect" ("nature, quality, character") and apply it correctly to your original example, we might comment that "the outstanding aspect of the translation was that it was powerful and accurate."

Keep in mind, then, that aspect tends to refer to the entire object.

If we look at your other noted definition of "aspect," we see "part, feature, phase." Again, the subtlety of interpretation of the meaning here is essential. Once again, these words are referring to something more allied with overall perceived identifications of the thing. Following are some examples. For feature: "One aspect (feature) of his work was its cleanliness." For phase: "In its later aspect (phase), the caterpillar is a butterfly." The important differentiation to make here, going back to your example, is that "aspect" would be referring to some perception of the finished product or entity on the part of an observer, whereas the characteristics you mention ("style" and so on) are really intended to be seen in this context as formative elements in the process of creating the translation.

For these reasons, "in every respect" is the correct usage, and importantly, it is the standard, expected, and well-understood phrase in this context. "In every aspect" is not used in this way; it would mean "in every perceived characteristic." (Think finished product, not creative elements.)