Defense Against the Dark Arts soon becomes everyone's favorite class. Potions, however, gets even worse for Neville once the story of Snape's appearance as a boggart gets around. Harry hates Divination the most, as Trelawney starts to cry every time she sees him. Nobody enjoys Care of Magical Creatures much, as Hagrid decides to teach the class to care for boring flobberworms. Fortunately, in October, Quidditch practice starts in earnest. Oliver Wood, the Gryffindor captain, holds a meeting one evening to tell the team that this is his last chance to win the Quidditch Cup before he leaves school.
When Snape actively starts to take revenge against Neville for what happened with the boggart, it indicates that Snape has no business teaching—he's not at all fair and cannot empathize with his students. Notice too that when Hagrid loses his confidence, the entire class suffers. This offers two ends of an extreme: while Snape can't teach because he's too confident, Hagrid can't teach (but isn't malicious) because he has no confidence.
One evening, Harry returns to the common room after practice to find everyone excited. Ron explains that the school announced the first Hogsmeade outing on Halloween and Harry throws himself into a chair. Ron suggests that Harry ask McGonagall for permission, while Hermione disapprovingly tells Harry to stay at school. Crookshanks interrupts the conversation by leaping into Hermione's lap with a dead spider. Ron tells Hermione to control Crookshanks, as Scabbers is asleep in Ron's bag. Without warning, Crookshanks leaps at the bag. Ron swings the bag around, sending Scabbers flying out the top. Crookshanks pursues Scabbers until Scabbers finds refuge under a chest and Hermione manages to catch the cat. Furious, Ron yells at Hermione and then stalks off to the dormitory.
While Ron has every right to be protective of his pet, he could also benefit from understanding that cats chase rats and it's part of their nature. In this way, what's happening here is no different than Buckbeak striking Malfoy when Malfoy insulted him. This indicates that, because Ron has such a personal connection to Scabbers, he's unable to take this wider view that cuts animals more slack for acting in accordance with their species.
Ron barely speaks to Hermione in Herbology the next day. When the class lines up later for Transfiguration, Harry notices Lavender Brown crying. Hermione asks Lavender what's wrong, and Lavender explains that Trelawney's prediction came true—it's the 16th of October, and she just got news that her rabbit died. Hesitantly, Hermione points out that Lavender only got the news today; the rabbit didn't die today, and Lavender wasn't dreading his death. Ron says loudly that Hermione doesn't care about other people's pets.
Hermione's unwillingness to accept Trelawney's prediction as fact suggests that Hermione trusts her own version of events and her own interpretations over those of someone who, to her, looks like a fraud. This shows that she doesn't think of Trelawney as an authority figure in the same way that she thinks of McGonagall or Dumbledore as being authority figures—she trusts what they say and takes them at their word.
At the end of Transfiguration, McGonagall reminds the class to hand in their Hogsmeade permission forms. Harry approaches her desk and asks for permission to go. McGonagall apologizes and says that she can't sign. In the hallway, Ron calls McGonagall names while Hermione looks as though it's for the best. Ron tries to cheer Harry up by reminding him of the Halloween feast, but it doesn't work. To make matters worse, even Percy admits that Hogsmeade is fun.
The fact that all Harry really wants is to go on a class trip with his friends reminds the reader that for all Harry's other problems, he's still a thirteen-year-old boy before he's anything else. His inability to see Hermione's point of view or take Sirius Black's threat seriously reinforces his youth and lack of maturity.
On Halloween, Harry feels very morose. Ron and Hermione even put aside their argument over Crookshanks to promise to bring Harry candy from Honeydukes. Malfoy taunts Harry about the dementors as Harry walks Ron and Hermione to the door and then wanders around the castle. He decides to visit Hedwig when he hears Lupin call his name. When Lupin ascertains that Harry is the only student not in Hogsmeade, he invites Harry into his office to see the class's next creature. He offers Harry tea and, with a twinkle, suggests that Harry has probably had enough of tealeaves. McGonagall informed him of Trelawney's prediction and he asks Harry if he's worried. Harry tells Lupin he's not, but decides not to tell him about the dog in Magnolia Crescent.
By inviting Harry in for tea, Professor Lupin begins to move their relationship towards one that's more personal. In doing so, Lupin shows Harry even more that he's someone who can be trusted, while his attitude and comment about Trelawney further discredit Divination as a subject. When Harry thinks of the dog in Magnolia Crescent, it shows that on some level, he is taking Trelawney's prediction seriously, as he appears to believe that the dog is the Grim.
Lupin asks Harry if there's something wrong, so Harry asks why he wasn't allowed to fight the boggart. He's surprised when Lupin doesn't deny it; Lupin explains that he didn't think Voldemort appearing in the staff room would be a good idea. Harry admits that he's more scared of dementors than Voldemort, which impresses Lupin—he says that this means Harry fears fear, and asks if Harry's been thinking that Lupin didn't think him capable of fighting the boggart.
The fact that Lupin tells Harry the truth shows that he believes his students deserve to be treated like adults and have their concerns taken seriously. When Harry is surprised that Lupin does tell the truth, it shows that up to this point, Harry has been able to expect that adults will keep things from him and treat him like a child.
Snape knocks on the door and lets himself in. He gives Lupin a smoking goblet, tells him to drink it now, and Harry notices a strange look on Snape's face. After Snape leaves, Lupin explains that he's been feeling a bit off and this potion is the only thing that helps. He praises Snape's skill as he drinks the concoction. Harry feels tempted to knock the goblet away and says that it's rumored that Snape is willing to do anything to get the Defense Against the Dark Arts job. Lupin expresses little interest in this.
Note that throughout the series, it's common knowledge for everyone—students and staff alike—that Snape wants to teach Defense Against the Dark Arts. This suggests that Harry isn't telling Lupin anything he doesn't already know, while Harry's suspicion indicates that he believes he knows more than the adults around him.
That evening, Ron dumps an armful of candy in Harry's lap and then he and Hermione tell Harry all about their Hogsmeade adventure. Hermione and Ron are aghast when Harry tells them about the potion that Lupin drank, and they wonder if Snape is trying to poison him. During the Halloween feast, the trio watches Lupin and Snape closely, but Lupin looks normal and Snape looks only a little on edge.
The thought that Snape is trying to poison Lupin is of course absurd, but it's easy to see why the trio would suspect this given how Snape treats them and how he seems to treat Lupin—though it is a huge leap to go from poisoning students' pets to hurting fellow teachers.
After the feast, Harry, Ron, and Hermione head back to Gryffindor Tower, but the hallway in front of the Fat Lady's portrait is unusually packed with students. Percy pushes to the front but drops his pompous attitude when he gets to the portrait hole. He sends for Dumbledore, who arrives nearly instantly, and Harry finally sees that the Fat Lady's portrait has been destroyed. Just as Dumbledore asks McGonagall to find Filch, Peeves floats overhead and cackles with delight. He says that the Fat Lady is hiding on the fourth floor and that Sirius Black destroyed her portrait when she wouldn't let him in.
The fact that the Fat Lady refused to let Sirius Black in shows how seriously she takes her job and her role as protector of the Gryffindor students. Again, this shows Harry that there are more people than he ever imagined at Hogwarts who are willing to help and protect him. In this case, even Peeves seems willing to play along and act like he's a good guy.