To kick this off, I put forward a few ideas and suggestions that will help you in the critique process.  I chose the letter 'I' to do this to remind us all that poetry is subjective and so is a critique.  What one person may love may leave another cold.  I have posted a poem in a few different poetry forums and received rave reviews in some and have had my work ripped to shreds in others. Remember when you critique the work of others, always be constructive and positive. Rather than say something offensive and hurtful, say nothing at all. When you express how you feel about a person's work, be careful to state 'I feel...' and 'I think...' rather than to say 'This poem is...' etc.  When you do make these statements, always substantiate your words e.g. 'I felt that this poem could have been more effectively rendered by...'  or 'I would suggest that you...' Always ask yourself the question 'How have I added value with this critique?'  Critique should always add value. Your intention should never be to hurt the feelings of the poet. It should be to encourage, to educate and to inspire. 

CRITIQUE

When you examine a poem you could use this checklist to help you to critique and provide constructive feedback
(Please scroll down):

Insight	A poem will often give us insight into a person's thoughts.  What does this poem tell you about the poet?
Interpretation	What was your interpretation of the poem?  What do you believe the poet meant for you to interpret?
Influence, Impact	How did the poem influence you?  What impact did it have upon you?  Describe from your own perspective remembering that this might not have been what the poet intended.
Ideas	Comment upon the ideas used.  Was the poet original?
Illustration	How well did the poet or writer illustrate his / her points?  If a poet used graphics to enhance his / her poem, how well did this fit?  Did the illustration enhance or detract from the poem?
Inspiration	Poetry can be very inspirational.  How were you inspired by the work?
Informative	How much information was supplied?  Was it enough?  Was more information needed to make the poem more meaningful?
Impact	This goes again to what kind of emotion was evoked when reading the poem.  Sometimes poetry is intended to elicit a response.  Sometimes the poet's intention is to incite rather than impact in a positive way.
Imagery	This is probably one of the most important factors to consider when reading poetry.  When you read the words, what images do you see?  How powerful and vivid were the mental images?  Could the poet have painted a more vivid picture?
Imagination, Innovation	It is important for a poet to use his or her imagination and to be innovative.  Use of cliches and hackneyed expressions greatly detract from the poem.  Originality is the key.  How effective was the poet in this area?
Impersonation	Was the poem in any way reminiscent of the poetry of another?  Again this goes to originality.  A poet should always strive to express naturally and should avoid copying the style of any other poet.  We may be influenced by poets we admire but our work should always be our own.  Careful never to plagiarize.
Inflection	How has the poet used patterns or stress and intonation in the poem?  Has this been effective?
Inflating	Has the poet tended to exaggerate or slip into hyperbole?  Sometimes this technique is used when writing comical poetry but it is important that the poet is careful not to 'over-ice the cake'.
Idioms	Check for use of idiomatic expression.  Has this worked in the poem?  Suggestions?
Intellect, intelligence	Although it doesn't take great intelligence to write good poetry,  a lot of thought should go into the writing or rather revision of a first draft.  Sometimes when I write creatively, I let my creative mind have free rein but I will invariably go back and put a lot of thought into what my words are saying, how they will be read by others and also into how the technical aspects of the poem work (e.g. rhyme if applicable, meter etc.)
Introspection	Is the poet being introspective or does the poem cause you to become introspective?  Poetry should always lead to reflection and this may lead to enlightenment.
Incomplete	One of the faults of many poets is to leave an idea incomplete or unfinished.  This can be effective but it is important that the poet completes his / her work.  Could the poet have completed his or her ideas better?  Were words missing? etc.
Impression	The poet entices a reader with the opening line and leaves an impression with the closing line.  Has the poem left you with a positive or lasting impression?  The impact of some of the poetry I have read in my life has left an indelible impression upon me.

This list is by no means complete.  You could probably add your own list.  Sometimes it helps to have a list such as this on hand just to remind you about what to look for.  You don't need to list all your responses in a review but this is a good guideline to poetry appreciation.  I hope it helps.