A good poetry review or critique can take about three steps, to allow a person to garner the most from what they are reading.
1) Clear your mind and read the poem through one time. Make notes on your initial impressions. If the meter or rhyme scheme slowed you down, make sure that is part of your notes. Does a particular image jump out of the words at you? Are you sensing romance, hatred, or another strong emotion from the writing? All of these things will be noted when you write your review. Keep a "This is great!" section, so that you can offer positive as well as constructive feedback.
2) Read the poem through a second time, paying close attention to the details the poet put into the poem. What images does the poem convey? Are they trying to give one scene or multiple scenes from the poem? Are they being metaphorical, satirical, or literal? Is there a background to the poem, which is necessary to put the writing in context for the reader? Concentrate here on the actual verbiage of the poem, what the poem is saying. If you had not tracked the meter and rhyme before, pay closer attention to it here.
3) Read the poem a third time, this time watching for mechanical, grammatical, and other base items. How consistent is the poet's punctuation? Do they constantly switch between tenses? Is something misspelled? Was that done on purpose? This is your last chance to look at the meter and rhyme scheme. You may want to make additional notes on it, if either is a serious enough flaw to damage the poem. As you work though this portion, noting things to praise the poet for not making a mistake with is always helpful.
Now that you've read the poem and made your notes, it's time to write the review. Remember that poets are human and they like to have their egos stroked now and then. Open with something from that "This is great!" section, or a positive impression that the poem gave you. Don't use all your compliments at this one juncture, though. Next, detail your suggestions for the problems you spotted within the poem. That is important to repeat. Detail your suggestions. The poet has the option to ignore your review so making your suggestions sound like demands or requirements will guarantee they won't be taken. If you are going to suggest items outside of the basic grammar rules, offering a reason why or helpful rewrite for a single line would also be beneficial. Do not rewrite the poem for the poet. Finally, take the last positives that you have saved up and close your review with encouragement and a few more strokes to the writer's ego.
As a final reminder, remember, the type of reviews you leave behind, dictate the types of reviews that appear for your own writing.