Yet turn, Old Year, before you go, And face your audience again. (line 15)
This "turn" matters a lot. This poem is about looking backward way more than it's about the future, so this turn back toward the audience is also a turn back into the past. In a way, it reverses time, because the year is supposed to march off without stopping. The speaker, who wants to hang onto the past for some reason, forces him to turn back. For just a moment he reverses the flow of time.
What hath the Old Year meant to you? (line 24)
Here the speaker is asking the people in the audience (and his own audience – that's us) to look backwards. He doesn't want to know what the new year "will mean." He's stuck in the world of memory, wanting to know what has come before. No judgment – that's not necessarily a bad thing, but it is a pretty distinctive feature of this poem.
What dark, condemning yesterdays?What urge to crime, what evil done? (line 36-7)
In this case, memory and the past aren't just a kind of wistful thing to muse about. They're really scary. The past is tormenting this poor guy. He can't get past it, can't think about the future. Things aren't nearly so bad for the rest of the folks in the audience, but still, the danger is there. The past can be a real trap, if we let it get that way.