Another quality I value is languaginess. It's when you sense in a piece of writing that sense that the poet was aware of the language used. Not just the choice of words (diction), but at the level of syntax and morphology.

I like too a certain enmeshedment, or feeling that the poem is tied to a certain place and time (and language) and cannot be taken out of there. Untranslatability would be a good word for this.

Constraintiness is another one. The sense that the poem is following invisible and mysterious rules, or visible yet still enigmatic rules. Constraintiness is not the opposite of freedom. In fact, they often are found in the same vicinity.

Not all poems I appreciate will have all these qualities, or have them in the same degree. For example I might like many poems that aren't constrainty in the least. I might like an anonymous lyric poem that is not distinctively written by a particular poet, etc... These are not criteria for poetry, but names for particular kinds of aesthetic pleasures. I would argue, though, that there has to be some kind of pleasure, whatever the set of names given it.