I asked the following question on Mi Yodeya, and later found an answer:

Question: After Eliyahu goes up to heaven, Elisha solves a water problem in Jericho and then heads to Bethel. On the way, some young children accost him, he curses them in the name of God, and two she-bears eat 42 of them (Melachim 2 2:23-24).

Rashi's comment on this is:

and some little boys: Heb. וּנְעָרִים, people empty [of any observance of commandments].

Go away, baldy: Go away from here, for you have made the place bald for us, for until now we would hire ourselves out to bring sweet water from a distance, and we would earn our livelihood thereby. And when the water became sweet, they lost their livelihood. Thus it is explained in Sotah (46b).

Even if Rashi's interpretation is correct, do people empty of observance (particularly children), whose proximate transgression is being mad about an economic matter, warrant being cursed and eaten by bears? I feel like there must be more going on here that I just don't understand.

What did the children do wrong? (Were they really children)? Did Elisha act properly in cursing them?

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Answer:

Bavli Sotah 46b-47a describes this incident in more detail. R. Yochanan said in the name of Meir that whoever does not escort others or allow himself to be escorted, it as if he shed blood, for if the men of Jericho had escorted Elisha, he would not have stirred up the bears. The g'mara then goes on to explain the incident.

First, who are the "little children"? The g'mara notes that "little" is redundant with na'arim and offers several possibilities: they were bare of precepts; they were little of faith; they were youths but they behaved like little children; perhaps they were from a place call Na'arah.

The g'mara also offers several opinions about what Elisha saw when he looked at them (a sage's gaze has special powers): that they were conceived on Yom Kippur; that they imitated Amorite customs/manners; that there was no sap of the commandments in them or in their future descendants.

All of that seems to suggest that, while the incident is regretable (if he'd been accompanied it wouldn't have happened), they in some sense had it coming. But then R. Hanina says that, on account of the 42 sacrifices Balak offered, 42 children were cut off from Israel, which makes it sound like they shouldn't have been killed (it was only because of Balak that they were). Further, Chazal taught that Elisha was afflicted with three illnesses, one of which was because he stirred up the bears, which also seems to be a condemnation of the event.

So my reading of this source, at least, is that the "children", who were probably some flavor of miscreants, taunted Elisha as Rashi described, and Elisha, with no one to help stay his hand and with the benefit of some special vision, over-reacted (and was later afflicted in punishment). They weren't exactly innocent, but their deeds didn't merit this death either.

Thanks to @gt6989b for pointing me in this direction.