Does the Phelps' farm episode in The Adventures of Huckleberry Finn differ in tone and seriousness from the first two-thirds of the novel?

Critics definitely argue that this final episode from the novel represents an "evasion" from the main themes and development of the novel up until this stage. It is definitely very comic, as Huck seems to become a sidekick again to Tom Sawyer, and Tom insists on showing his true Romantic self by devising a ridiculous escape plan so that they can rescue Jim in the way that "all the books" say he must be rescued. One can't help but be amused at Tom's insistence that they carry out the escape plan "properly" rather than follow Huck's incredibly simple, straightforward and effective idea. Note how Tom Sawyer responds to this practical idea:

Work? Why, cert'nly it would work, like rats a-fighting. But it's too blame' simple; there ain't nothing to it. What's the good of a plan that ain't no more trouble than that? It's as mild as goose-milk. Why, Huck, it wouldn't make no more talk than breaking into a soap factory.

So it is that Tom Sawyer suggests his ludicrous plan that Jim himself has to come out of his "cell" to help with. However, whilst there is a definite change of tone, I believe it is possible to argue that there is a much more serious underlying tone going on in this final episode of the book. Note the way that Jim is treated by Tom's plan. Tom is more concerned about doing the escape "right" than he is about Jim's welfare. In particular, critics point out his cruelty in not announcing that Jim had actually been released until after he had had his fun in devising the escape plan and carrying it out. The pervasive theme of racism is still very much present even in the final chapters of this book.

Does the tone and seriousness of Phelps' Farm episode differ from the rest of Huckleberry Finn?

These sections of the novel are different, but not necessarily in tone. The entire novel is comical, farcical, whimsical, and full of adventure. Throughout the novel, the characters fail to appropriately or fully assess reality and deal instead in some semblance of fantasy. 

The change that takes place in the last section of the novel has to do with Huck Finn's awareness of his own folly and his willingness to make this awareness known in the narrative. 

We can see a similar tone in Huck's narrative in two particular episodes. Early in the novel Huck watches Tom Sawyer and other townspeople as they fire cannons from a boat while searching for Huck's supposedly dead body. 

When the boat comes close, Huck is almost killed by a cannon blast:

Then the captain sung out: "Stand away!" and the cannon let off such a blast right before me tht it made me deef with the noise and pretty near blind with the smoke, and I judged I was gone.

The irony of this situation (Huck is nearly killed while watching people search for his dead body) is parallel to that of one of the book's final episodes. 

When Tom awakes after days of sleep after he is shot, he announces that Jim is a free man and has been free since Tom arrived at the Phelps house. 

All the antics and adventures performed to free Jim from bondage were completely unnecessary. Jim was already, ironically, free. The connection between these episodes demonstrates a continuity of tone through the novel. The text is, for the most part, always humorous, fast-paced, and dependent on folly and fraud for its action. 

Tom Sawyer continues this folly and fraud in the final section of the novel. 

In the last third of the book, Huck defers to Tom Sawyer, whose outlandish schemes to free Jim direct the action. Huck is no longer in charge, and his moral quest appears to have been abandoned.

What separates the latter section from the earlier one is Huck's attitude. Huck decides to go against society's code of moral law and to free his friend Jim if he can before Tom Sawyer arrives. His major conflict has been resolved, it would seem. However, Tom Sawyer is a subtle stand-in for the society that Huck has attempted to free himself from, morally speaking, and the dominance of Huck's conscience continues through Tom. 

In this section, Huck does not rebel beyond a certain point against Tom and the society (moral authority) he represents. Instead, he demonstrates an ambivalence toward this authority. This ambivalence is new. Where Huck once agonized over right and wrong, he now muses on the folly of accepted wisdom.