The new judge-who didn't know Pap and what a loser he was-refuses to let Judge Thatcher or the Widow adopt Huck because he idealistically didn't want to "take a child away from its father". Later, the new judge takes Pap into his home to "make a man of him". He thinks he's succeeded (Twain very humorously describes the new judge and his wife weeping with joy at the success of their reformation), until Pap trades his clothes for whiskey and nearly freezes to death after falling off their porch in a drunken stupor. Finally, the new judge comes to the realization that "a body could reform the old man with a shotgun maybe, but he didn't know no other way". So, the judge finally realizes what Judge Thatcher and the widow already knew: what a loser Pap was.
Twain is making fun of do-gooders, who come in on their white horses thinking they can save the entire world; he does this by using Pap to give the new judge a harsh reality check. The judge's end opinion falls in line with what a young Huck already knew, that some people are pretty hopeless.
Twain satirizes do-gooders--more politely known as philanthropists--in his description of the extravagant, tearful sentimentality displayed by the new judge and his wife in their attempts to reform Pap Finn. For instance, when Pap solemnly gives them his hand to shake, the judge's wife is not content with just doing that, she also kisses his hand. Twain plays up the complacency, not to say pomposity, of people like this judge who appears confident not just of reforming Pap but doing so literally overnight. He gets a rude awakening when Pap repays all his efforts by getting hopelessly drunk, climbing out of the house and falling and breaking his arm. Therefore Twain shows just how useless do-gooders can be. In this instance, the judge is completely taken in by mere appearances, when Pap seems to be so ashamed and repentant, making a long solemn speech about how he's going to turn over a new leaf. His actions don't even begin to correlate with his words, however.
Twain often took 'do-gooders' to task in his writings--members of temperance societies, prison reformers, and the like. He shows them as being often exaggeratedly sentimental and affected, and hopelessly unrealistic in their expectations of bettering individuals and society.