The Limits of Imitatio Dei

1700 years ago (as recorded on Sotah 14a), Rabbi Hama, son of Rabbi Hanina, said

מאי דכתיב אחרי ה' אלהיכם תלכו וכי אפשר לו לאדם להלך אחר שכינה והלא כבר נאמר כי ה' אלהיך אש אוכלה הוא אלא להלך אחר מדותיו של הקב"ה.
מה הוא מלביש ערומים דכתיב ויעש ה' אלהים לאדם ולאשתו כתנות עור וילבישם אף אתה הלבש ערומים
הקב"ה ביקר חולים דכתיב וירא אליו ה' באלוני ממרא אף אתה בקר חולים
הקב"ה ניחם אבלים דכתיב ויהי אחרי מות אברהם ויברך אלהים את יצחק בנו אף אתה נחם אבלים
הקב"ה קבר מתים דכתיב ויקבר אותו בגיא אף אתה קבור מתים

What is meant by what is written: "After the Lord your God you shall follow"? Is it possible for a person to walk after Shekhinah? Behold! It has already been said, "For the Lord your God is a consuming fire." Rather, one should follow after the Holy One, Blessed be He's characteristics:
- Just as He clothed the naked, as it is written, "And Lord, God, made garments of skins for the man and his wife and clothed them," so shall you clothe the naked.
- The Holy One Blessed be He checked in with the ill, as it is written, "And the Lord appeared to him at the terebinths of Mamre," so shall you check in with the ill.
- The Holy One Blessed be He comforted mourners, as it is written, "And it was after the death of Avraham, God blessed Yizhak, his son," so shall you comfort mourners.
- The Holy One Blessed be He buried corpses, as it is written, "And He buried him in the valley," so shall you bury corpses.

Although the primary task set before Rabbi Hama here is to synthesize these texts, his resultant synthesizing produces a way to follow not after God, per se, but rather His characteristics. The issue that then faces us is to then figure out in which other ways we are supposed to do so (unless Rabbi Hama was not merely providing examples, but saying that just these specific actions are to be followed).
But if so, how expansive is the range of actions of God are we supposed to follow? Although I certainly don't have an answer, there seems that there is probably a limit.

In one of his postings last week, Professor Shapiro points out a lecture from 2006 at the University of Scranton, which includes, as a respondent, Rabbi Aryeh Klapper, whom Shapiro references as "one of the most enlightened and thoughtful spokesmen for Modern Orthodoxy." Towards the end, Rabbi Klapper makes a point about the limits of imitatio Dei:

It’s a good question – it’s a question that I think is tied up with the notion of what it means to imitate God. There’s a very interesting Talmudic statement that says that just as God is merciful, we should be merciful, just as God is kind, we should be kind, just as God buries the dead, so, too, we should bury the dead, all sorts of things like that. The problem is that God doesn’t just bury the dead, God kills the dead. And God isn’t just merciful, God is cruel.
So I think that, at least the Jewish tradition has made a conscious effort to say that the goal of a human being is not to be God. And there are things that God does that we say that God has a right to do and we can perhaps do when God tells us specifically to do them. We can carry out certain punishments when God authorizes us to do them, but I don’t think that means …
God brings famine; I don’t think that justifies Stalin – in starting the collectivist farmers for a greater good. I think that using Divine actions as our model except when our tradition tells us specifically that these Divine actions are supposed to modeled in specific ways is – I would describe it as acts of spiritual arrogance overall and, for myself, it would be scary to conceive of myself as capable of doing everything God can do and having it come out right.

I may have more on this later, but Rabbi Klapper makes some interesting points here.