The next day, Harry sees teachers putting security measures in place. McGonagall fires Sir Cadogan and the Fat Lady returns with security trolls to guard her. Harry notices that the statue of the witch that leads to Hogsmeade remains unguarded, but Ron insists that Sirius Black can't be getting in through Honeydukes. Ron becomes a celebrity overnight, though he doesn't understand why Black ran instead of murdering the entire dormitory. Neville is disgraced and McGonagall forbids anyone to give him the passwords. He also receives a Howler from his grandmother one morning.
Again, Ron is still correct that Sirius Black isn't using that particular tunnel, but that doesn't mean that the tunnel isn't still a liability—especially since it's implied throughout the novel that not all the teachers know about the tunnel, which means that the students might not be as safe as the staff would like to think they are.
As Harry watches Neville run away with the Howler, Hedwig nips him so he'll take her letter. It's from Hagrid inviting him and Ron to come for tea in the evening. Ron is excited to get to tell Hagrid about his heroism, but Hagrid is uninterested. In Hagrid's cabin, they notice Buckbeak on the bed with Hagrid's awful brown suit, all ready for Buckbeak's hearing in front of the Committee for the Disposal of Dangerous Creatures. Harry feels guilty; he forgot about the trial.
When Harry realizes that he's let Hagrid and Buckbeak down in regards to the trial, it shows him understanding that a true friend doesn't forget this sort of thing. By recognizing this, Harry will be able to use the shame he feels here to change his behavior going forward and, hopefully, be a better friend.
Hagrid looks uncharacteristically serious as he says that they need to talk about Hermione. He says that she's been visiting him often to help with Buckbeak's case, though she often cries because she has so much on her plate and Ron is ignoring her. Hagrid says that he thought Harry and Ron would value friendship more than objects. Ron angrily says that he'd speak to Hermione if she got rid of Crookshanks, and then the conversation turns to Quidditch.
With this, Hagrid is able to use his role as a friend, a mentor, and a teacher to give the boys the hard-hitting talk they need to hear about friendship. By encouraging them to put Hermione first, he gives them a boot towards adulthood, maturity, and in Ron's case especially, forgiveness.
When Harry and Ron return to the castle, they see that a Hogsmeade trip is scheduled for next weekend. Harry quietly says that the passage isn't blocked up yet, but Hermione appears behind them and threatens to tell McGonagall about the Marauder's Map if he goes to Hogsmeade again. Ron tells Hermione to leave it alone and Hermione leaves when Crookshanks jumps into her lap. Harry agrees to go with the Invisibility Cloak.
To Harry and Ron, Hermione's threat appears mean, but to the reader (and to any adult who might learn of the map), Hermione is fully justified and doing the right thing by making this threat. She cares for Harry's safety and knows that he's not taking it seriously. Therefore, as his friend, it falls to her.
Harry goes to breakfast with everyone else on Saturday morning, the Invisibility Cloak and the map in his pockets. After everyone else leaves, he heads for the third floor and checks the map by the witch statue. He sees Neville coming and can't get himself through the passage before Neville appears. Neville invites Harry to play a game and work on their essays for Lupin, but Snape interrupts. His eyes flick to the witch statue as he sends both boys back to Gryffindor Tower. Harry ditches Neville at the portrait hole and then races back to the witch statue and climbs in.
When Snape's eyes flick to the statue, it suggests that he's aware that the statue protects a tunnel leading out of school. This makes him a dangerous enemy for Harry should things go wrong, as Snape then has more proof that Harry is misbehaving and disregarding adults' attempts to keep him safe.
In Hogsmeade, Harry finds Ron. They decide to visit the Shrieking Shack, one of the most severely haunted buildings in Britain. Suddenly, they hear voices and see Malfoy, Crabbe, and Goyle approaching. Malfoy is talking about Buckbeak's hearing and when he sees Ron, he teases him that the Shrieking Shack would be more luxurious than the Weasleys' house. Harry sneaks behind Malfoy and throws mud at him. Ron, laughing, remarks on how haunted the Shrieking Shack is. Harry throws more mud at Crabbe and Goyle and Crabbe runs at Harry. Harry sticks out his leg to trip Crabbe, but Crabbe's foot tugs the cloak off of Harry's face. Malfoy screams and runs.
Out in Hogsmeade and away from teachers, Malfoy feels free to bully Ron mercilessly—there's nobody to stop him from being a jerk and while he’s "alone," Ron is defenseless. While this does show that Malfoy is very tuned into the social structures around him and knows how to play them to his advantage, it also indicates that he's aware of his lack of power—unlike Snape, Malfoy can't torment Ron or Harry openly, as he doesn't have the prestige afforded to teachers.
Harry races back to Honeydukes and hopes that nobody will believe Malfoy. He decides to leave the cloak in the tunnel and just as he closes up the passage, Snape appears. Harry guiltily sticks his muddy hands in his pockets and follows Snape to his office. Snape tells Harry that Malfoy saw him in Hogsmeade. Harry tries not to blink and suggests that Malfoy was hallucinating, but Snape won't have it and Harry is forced to admit that nobody can confirm that he was in Gryffindor Tower.
In this situation, Harry is in especially deep trouble since Snape hates him so much. Because of this, Snape doesn't need to find much proof to feel justified in punishing Harry, and Snape will believe Malfoy before he listens to anything Harry has to say. This shows that even within Hogwarts, justice doesn't always function fairly.
Snape says that even though everyone is trying to keep him safe, Harry doesn't care about consequences. He says that Harry is just like James and that James didn't care about rules either. Harry snaps, tells Snape to shut up, and says that Dumbledore shared that his dad saved Snape's life. Snape asks if Harry knows the details. Harry doesn't, so Snape says that James and his friends played a joke on him that could've killed him; James was saving himself from punishment by "saving" Snape.
While Snape tells Harry these things about James specifically to provoke Harry, it's worth noting that Snape has a point: Harry isn't taking Sirius Black seriously, and he's disrespecting every adult who's trying to keep him safe by breaking their rules. However, because these words come from Snape's mouth, Harry is less likely to believe him.
Snape asks Harry to empty his pockets. Harry pulls out his shopping bag from Zonko's and the Marauder's Map. He tells Snape that Ron gave him the Zonko's items as Snape picks up the parchment and starts to throw it in the fire. When Harry jumps, Snape hits the map with his wand and tells it to reveal its secrets. Words appear on the map, all insulting Snape's appearance. Snape summons Lupin through the fireplace and Lupin climbs out. He inspects the map and says it likely came from Zonko’s, but Snape says it must have come from "the manufacturers." Lupin asks Harry if he knows Moony, Wormtail, Padfoot, or Prongs, and Harry truthfully says he doesn't. Ron bursts in, out of breath, and says he gave Harry the Zonko's products a while ago.
Snape's suspicion of the map and his mention that Harry got it from the manufacturers again suggests that Snape has information that Harry doesn't. When Lupin gives Harry the opportunity to tell the truth, he helps Harry's case by giving him at least one shred of truth to hang onto. Then, when Ron insists he gave Harry the Zonko's products, it indicates that Lupin is actively helping Harry and saving him from Snape's ire—there's no way he could've known that Snape was the professor to intercept Harry without help, as all professors are dedicated to keeping Harry safe and in the castle at this point.
Lupin cheerfully takes back the map and tells Harry and Ron to follow him. In the entrance hall, Lupin says he knows that the parchment is a map and is aghast that Harry didn't turn it in. Harry asks why Snape thinks he got it from the manufacturers. Lupin hesitantly explains that they would've found it entertaining to lure Harry out of school and admits that he's met them. He says that he won't cover for Harry again and says that Harry is doing a poor job of repaying Lily and James's sacrifice. Harry feels awful. As Harry and Ron reach the corridor for the portrait hole, they see Hermione coming towards them. Ron meanly asks if she told on them, but she shakily says that Hagrid lost and Buckbeak will be executed.
While Lupin says much the same thing that Snape did by bringing up all the people who have tried to keep Harry safe, it has more of an effect coming from him since Harry trusts and likes him. This shows how good teachers have a great deal of power, even when they reprimand students—their disappointment carries more weight, as Harry desperately wants to impress Lupin and be worthy of his respect. The effect of Lupin's words suggests that Harry will take them to heart going forward.