I disagree with the answers saying a poem can be "too perfect" or "mechanical sounding" when the rhyme and meter are perfect. Poetry is an art, and like all art forms, there are certain boundaries and expectations that set it apart from what is not art (assuming that some things are not art).
With too loose a definition, everything is poetry. Advertisements, text messages, sports announcements, movie scripts, even things like dance can all be considered forms of poetry.
For me, meter is a sort of mantra. Iambic tetrameter can practically send me into a trance state when done well enough. Look at "Stopping by Woods on a Snowy Evening." Robert Frost wasn't a big fan of perfect meter, but when he did it in that poem, the effect was an elevation of common language into the realm of high art.
The problem with perfect meter is that it's hard to pull off without forcing or distorting syntax and language. When people try to write like that, they often end up sounding archaic, which can ruin the reading experience of a poem.
But to answer your question, a poem with perfect rhyme and meter can (and is more likely to) be flawed in many ways. First, it must succeed in all of the challenges that come with any poem (content, meaning, language, tone, mood, technique) and second, it must use the meter and form correctly. Using anapestic tetrameter where you should have used iambic pentameter would result in a train wreck.
If a rhymed verse poem is "imperfect" in meter, the imperfections should create some kind of intended and appropriate effect. Two stressed syllables next to each other, for example, to create tension or emphasis. Two unstressed syllables next to each other to create rapidity and smoothness.
"Sainuvomoro's" comment about the teacher upsets me. I've met so many people who don't appreciate or understand the appeal of rhymed verse. They'll say that it all sounds like Dr. Seuss or like nursery rhymes. It's so belittling.