That said, here are some thoughts on preparing yourself to be a poetry editor:
1) Get to know poetry. The more you read, the better your discernment will get, telling you what is good and what isn't. Read both classic and contemporary poems. If you have the opportunity, go to a live poetry reading. Watching "Def Poetry" on HBO is almost as good. However, do not be too swayed by other people's opinions; the contemporary poetry scene is cluttered by lauds of poetry that is not really laudable. Develop your own judgment.
2) Study the literary techniques used in poetry, so that you'll understand how they're supposed to work and thus have a better idea what can go wrong and how to fix it. Useful books include Creating Poetry by John Drury and Dictionary of Poetic Terms by Jack Myers & Doc C. Wukasch. My forthcoming book Composing Magic has chapters on poetry and poetic techniques, with a special focus on magical/Pagan poetry. A good glossary of poetic terms and techniques is here.
3) Talk about poetry with other poets and editors. It's fun, and broadens your analytical skills. This blog is just one of many places suitable for that. The Poet Sanctuary has a forum for critiques of poetry where you can practice those skills.
4) Join one or more poetry organizations. Some good ones include the Science Fiction Poetry Association and the Academy of American Poets.
5) Watch for poetry workshops, panels, and other activities at whatever events you attend. Pagan festivals and science fiction conventions occasionally have poetry-related activities. With the right group of people, you can learn a lot in just one or two hours.
6) If you publish a lot of poems, write up specialized submission guidelines for poetry. Mention how much you pay per poem, bearing in mind that better rates tend to attract better quality. Be specific about your market's target audience and what kind of poetry you want. Detail helps contributors hit your target. However, don't tighten the focus so much that the material becomes repetitive -- leave room for your contributors to surprise and delight you. Compare your poetry guidelines with those of other markets; talk about them with your editor-friends. Mine for PanGaia are here.
7) Make sure the contract for your poets is both clear and fair.
Now, here are some thoughts on selecting and fine-tuning poems for publication:
1) Read your slush pile when you are alert, comfortable, and generally in a positive mood. That way, you give each poem the attention it deserves. If you're tired, sick, cranky, or otherwise not your best then you may miss something good or be unnecessarily harsh with contributors.
2) Make sure the poem follows the rules of its form. If it's supposed to have a specific meter or number of syllables, count them on your fingers if that's what it takes. If it's supposed to rhyme, the rhymes should be perfect unless the poet deliberately uses near-rhyme in a consistent way. One online guide to poetic forms is here. A good hardcopy guide is The Book of Forms by Lewis Turco.
3) Seek for meaning and clarity in the poem. It should have a definite theme. Its mood should be consistent and appropriate for the theme. "Mysterious" and "murky" are not the same; mystery can be attractive, but murk is off-putting. A high-impact poem, one that gives you a real jolt when you read it, is a poem you should seriously consider accepting. On the other hoof, if you can't figure out what the poem is about, reject it.
4) Sometimes a very good poem will have just a few flaws, like extra syllables or an unclear line. Don't be afraid to suggest improvements, or request that the poet make changes to fix a specific flaw. Don't be afraid to edit poetry. In fact, don't be afraid of poetry!
5) If you think you want to accept a poem, read it out loud. A worthy poem should make you want to do this anyhow, and it should feel good in your mouth and ears when you read it. Some of the best examples for mouthfeel and earcharm come from poets who wrote mainly for children, such as Shel Silverstein and Dr. Seuss, but there are some good grown-up examples too, like Edgar Allan Poe and e.e. cummings.
6) Do give feedback, especially if the poet requests it. The same rules for targeting information apply to poetry as to fiction and nonfiction. Basically, be gentle if possible, firm if necessary, and always honest. Treat your contributors with respect, remembering that today's ugly duckling may be tomorrow's swan. A few minutes coaching the "almost good enough" poets can save you and them from wasting time on the same mistakes over and over again. Part of an editor's job includes helping the promising new writers develop their craft.
7) Pay attention to your budget. It doesn't have to cost a lot to attract good contributors and a lively audience.
That about covers the basics of being a poetry editor. Like all skills, editing poetry is something you'll get better at over time. If you're thinking about including poetry in a market you already edit -- please, go for it! You can start small, just printing one poem at a time, and expand if you like the results. Poetry is a treasure that grows more valuable the more you share it.