Under what circumstances does God act on His anger? While there is some debate over whether God is angry or loving (or both), it is clear that God sometimes acts on His anger with wrath and vengeance, and other times He does not. Do we know the criterion by which He makes these calls? Can we even pretend to know?

Because if we can't, then we have no way of knowing whether He is a God of love or anger. For example, maybe He's letting people He's angry with live so as to teach us a lesson, or to test our faith in Him. So it would be for the greater good, and thus an act of love. But maybe He's letting those people He's angry with—and other sinners—live as punishment to us, such that we have to endure them. Simply put, if we cannot speak to why He smites some and not others, if we don't have any idea of the criterion He uses, it's impossible to know if He is completely loving or completely hating, or somewhere in between.
By definition God is love, but sometimes you have to punish if you love, and when God is angry it isn't a sense of passion that drives Him, but judgement of justice, as explained in Objection 1 of Summa Theologica, Q47 (http://www.newadvent.org/summa/2047.htm).

I think the difficulty is that you are trying to relate your anger to God's anger, and making His anger to be similar, or comparable, to ours.

This is a problem as God is angry at the sin and the sinner, but, He understands perfectly what is going on, what the motives are, and at times may need to punish in order to help try to rectify the actions.  

There is nothing wrong with being angry.  Jesus was angry, for example.  It is an emotion, but why someone gets angry and what is done with the anger is the issue.

We can't judge why God chooses to get angry at one and not at another, as, much like a mosaic, you see only a tiny bit of the picture, so the best we can do is to have faith that God has a reason for what He chooses to do or not do.

For a longer discussion on Is God Angry Anymore?, you can read:

http://www.ccwtoday.org/article_view.asp?article_id=18