Plot: following reports of a purse-snatching leprechaun, Batman discovers the Sewer King and his gang of orphan thieves.
Really, this episode is about Batman's relationship with children, specifically orphans. As with Nothing to Fear, The Underdwellers assumes you already know that Batman is himself an orphan, and identifies with the Sewer King's victims (there's a sideways allusion when Batman yells "children and guns do not mix. Ever!" It's such an obvious point that it hides the fact that Batman is referring to a specific event).
We also see children's reaction to Batman: they think he's cool, obviously. Frog may run from Batman at first, but he learns to trust him, first when Batman saves his life, again when he sees a trash bin transform into the Batmobile, and again when Batman says he needs Frog's help. (Props to the animation and music departments. Since the Underdwellers don't talk, their acting is done through facial expression and music cues, and done quite well.)
But Batman does more than protect and comfort children, he also inspires them. The key scene, really, is when the Sewer King threatens to feed one of his own children to the alligators is Batman does not back off, Frog swings down on a rope in a Batmanly manor and saves the kid himself, earning the world's greatest honor, the Bat-thumbs up!
If anything, that's what's missing from the episode. We see Batman the son, identifying with Frog and sympathizing with the other orphans. But where's Batman the father? Robin isn't mentioned at all, but Robin is evidence that Batman has a habit of taking in orphans and turning them into superheroes (by this time in the comics, he would have done it three times already, and will do it again later in the Animated Series). From the way Frog swings on a rope, it wouldn't have surprised me if they made him the next Robin, or if his real name were Jason Todd.