I think there should be a high level of communication and connectivity, so that, even if the intended meaning is completely lost on them, the reader can more easily see their own meaning in the piece. I'm a creative writing major in my final year of college, and i cannot tell you how many poems I've had to read that just seemed to go over my head. But I had to read them, because they were "good pieces" and, I'll admit, they were extremely well written. However, the only pieces that I felt myself drawn into and really influenced by were those I could connect to, or at least communicated to me the poems intent.
One of the first poems I read in college, and one of my favorites to this day, is "This Is Just To Say" by William Carlos Williams. It's only twelve lines long and is one of the most straightforward poems I have ever read:
I have eaten
that were in
you were probably
they were delicious
and so cold
It's silly and strange, but I love it because it communicates its purpose so well, and i can so easily connect to it, because i have left notes like this myeslf.
But I'm getting off topic, so I'll wrap it up: communication is, to me as a writer and as a reader, of utmost importance. It shows effort on the author's part, both the effort to get his or her point across and the effort that we, as the reader, take away something from the piece.