This is not going to be a comprehensive essay on everything one needs to do in order to review poetry as I would not presume to be in the position to write that essay.
My views are impressions taken from my two months at Fan Story and offer nothing more or less than opinions based on my experience. Please take from them what seems of value and discard what goes against your better judgment.

As a poet, the first thing I respond to on a visceral level when reading a review is if the reviewer seems to have "gotten" what I had to say. Whether I am told the reader has experienced similar joys or has taken away from my piece some sort of reflection matters a great deal to me. Most poets, I believe, write to connect to their audience on a deeply human level, and so to know we have been "heard" makes all the difference. If a reviewer agrees or disagrees with me matters not, just so he or she has responded on some emotional or intellectual level.

If this does not occur, if the reviewer jumps immediately to telling me what syllable of what line of what verse was accented wrong, I go into defensive mode.
Please do tell me what word did not fit the mood of the rest of the poem or what line broke with the established rhythm, but if that is all you tell me, I start wondering why in the world I failed so terribly in making you feel or think. I have received reviews, not many I'm glad to report, where the reviewer never mentioned at all what the poem was about. I have received some, not quite as stilted, which say something like, "Nice discussion of fairies" and then launch into two paragraphs of critique of metering and rhyming, never to mention a fairy again.

It is a matter of balance. Yes, as a writer I do welcome any advice as to technique and style, but technique and style are employed for one reason and one reason only, to enhance what a poem has to say. The poem rhymes or flows in service of the content. I've yet to meet a poet who wrote solely in order to get the form right. Poetry is not an intellectual exercise in meeting the challenges of a form. It is using a form that allows the words to sing.

Another issue that arises when I read reviews is that some people would impose their preferences for one form or stylistic choice over another on the poets they review. I have seen this in reviews of other poets in addition to reviews of my own work. One poet, not I, clearly labeled her work a villanelle, which requires the repetition of certain lines in a given pattern. The reviewer docked a star because he does not like repetition. It is clear that person should never then write a villanelle or pantoum or triolet, but neither should he review them if he is automatically going to grouch at any repetition. It is certainly conceivable that a poet's use of repetition did not work well in one of these forms, and then the reviewer should point out which line did not work, but one can't tell another writer to stop using a form altogether.

My first experience with this problem arose when reviewers pointed out to me each instance of rhyming that was not exact in nature - when I would rhyme roam and lone, for instance. Again, if my near rhyming does not work at times and seems off in a particular line, please let me know. But do not impose on me a requirement that all my rhymes be exact rhymes every time I write as if they were errors otherwise. I wrote another essay on this site about the issue of rhyming weeks ago where I pointed out that poetry has a grand tradition of poets who have purposely employed near rhymes. To assume my near rhymes are always mistakes to be corrected, with an offer to reread my poem after I correct the errors, is off-putting. A reader who does not ever like near rhymes should, of course, in her own poetry, keep to exact rhymes.

This brings up another issue - please don't review a person's poetry because of what it does not mention. I wrote a humorous story poem of a lazy man who rocked his life away which most readers enjoyed. One reviewer told me he also enjoyed it, but he wished I had written additional verses giving the views of the lazy man's friends and relatives. For this he docked a star. Perhaps his idea was a cute one, but my failure to have the same vision he did of my story did not prevent my poem from being funny and it did not render my story hard to follow or incomplete. If you write a poem about wildflowers in a meadow and write lovely descriptions of buttercups and violets, it is not my place to lower your score because you did not also include a verse about daisies, my favorite flower. I should review you on what you did choose to write about. Should a reviewer prefer a poem about daisies, that person should take pen in hand and write that poem.

Please tell me if my ideas are clear, if they aroused some sort of passion or made you laugh or caused you to reminisce. Please tell me if you were diverted from appreciation of the poem's message because a line got muddled or a rhyme was just a clunker. Poets are emotional sorts who are extremely invested in their writing, but they are also craftsmen, and should be able to take a little criticism. But we are human to the core. Peggy Tabor Millin once said, "We never touch people so lightly that we do not leave a trace." When you touch a poet with your review, please keep in mind that you are not just reviewing four quatrains or rhyming couplets; you are reviewing the person who composed them. Honest criticism makes us better writers, but honesty tempered with a human touch is never too much to ask.