"Together you and I are worth the front page."
-- Gilderoy Lockhart
Harry and the Weasleys receive their required book lists from Hogwarts and go to Diagon Alley via Floo powder. There Harry arrives in Knockturn Alley, overhears the Malfoys, is found by Hagrid, meets author/teacher Gilderoy Lockhart, and Arthur Weasley comes to blows with Lucius Malfoy.
Calendar and Dates
The main action of this chapter occurs on the August Wednesday on which the Weasleys and Harry visit Diagon Alley. Using the real world calendar for August in 1992, we can surmise that this happened on August 19.
Interesting facts and notes
As hinted at by the chapter title, the main event of this chapter takes place at Flourish and Blotts: Lucius Malfoy planting Riddle's diary among Ginny's schoolbooks. Lockhart's grandstanding serves primarily as a contrast to Harry's attitude toward his own rather more substantial claim to fame, while the fistfight between Lucius and Arthur is only one (rather dramatic) demonstration of their very different attitudes toward Muggles.
Life at the Burrow was as different as possible from life in Privet Drive. The Dursleys liked everything neat and ordered; the Weasleys' house burst with the strange and unexpected.
Harry isn't the only witness to the Dursleys' overly fussy, rigid approach to neatness. Tonks will observe three years later that the Dursleys' place is "a bit too clean" (OP3).
Neatness per se isn't represented as a bad thing in the Harry Potter universe; when reasonably satisfied with their situations, for example, house-elves (such as most of those on staff at Hogwarts, and Winky before her dismissal from the Crouch household) are uncommonly tidy, while unhappy house-elves may do their work neatly but do not keep themselves tidy. Hermione is devoted to organization - even in her first year, she colour-coded her notes and drew up study schedules - but that serves a purpose in her case.
The kind of neatness practiced at number four, Privet Drive, though, is sterile and rather pointless (also note observations in OP2 about Petunia's "surgically clean kitchen"). The Dursleys mainly seem interested in conforming to some ideal of normalcy, rather than, say, just keeping the house organized to make life comfortable for the inhabitants. Petunia keeps a very clean house, but is never mentioned as having other interests apart from spying on the neighbours and fussing over her son. Even then, as observed by Harry in GF2, Petunia is quick enough to spot fingerprints on her gleaming walls, but fails to see some very obvious, important things (Dudley's dangerous obesity).
small explosions from Fred and George's bedroom were considered perfectly normal
This certainly constitutes underage magic, but no one seems to care. Why Fred and George were disappointed at the end of the last term when they were given their Ministry warnings about this sort of thing is unclear, since they obviously ignore them and get away with it.
Harry talked him through using a telephone
Arthur apparently teaches the rest of the family this Muggle skill. The next summer, Ron gives the "fellytone" a try and calls Harry in Privet Drive. However, he shouts so loudly that Uncle Vernon is incensed. Then Ron identifies himself as a member of the magical community, whereupon Vernon hangs up on him. Even Molly learns to use the phone, however, because a year later she "brave(s) the telephone in the village Post Office" to order taxis to take them to Kings Cross.
Five minutes later they were marching up the hill, broomsticks over their shoulders. They had asked Percy if he wanted to join them, but he had said he was busy.
From this, we gather that Percy can play Quidditch if he wants to, although we don't know what position (if any) he prefers to play. Also, we can see that Percy's brothers are trying to be friendly with him, but he's too preoccupied to be interested in family Quidditch games.
The boys don't seem to have thought to ask Ginny if she wanted to play, unfortunately. How they underestimate that girl...
"He's not himself. His exam results came the day before you did; twelve O.W.L.s and he hardly gloated at all."
Several pieces of information can be worked out of this remark.
Percy can ordinarily be expected to gloat over an achievement (compare his lack of response over his O.W.L.s with his making sure everyone knew he'd been selected as a Gryffindor prefect the previous year, or with his laying stress on his Head Boy status the next year), but he's preoccupied with something else this summer. As Ginny reveals on board the Hogwarts Express in C18, Percy now has a girlfriend, Penelope Clearwater, and has been writing to her.
Two of the Weasleys, in fact, are not behaving like themselves this summer - Ginny and Percy - and until the visit to Flourish and Blotts, it's for the same reason, although the reason is an open secret in Ginny's case while being hidden in Percy's: each has developed a romantic attachment to someone else. In Ginny's case, of course, she has become very taken with Harry, which is later used to distract the reader from her diary-influenced activities. In a nice piece of symmetry, though, Percy's obviously suspicious behaviour is covering up the fact that he's courting Penelope Clearwater. Notice that throughout the book Percy is dragged across the readers' path as a red herring when diary-related activity crops up.
On another note, the O.W.L. results in 1992 [Y12] were reported back to the students on 3 August, not in July, so it appears that the time of delivery of O.W.L. results varies from year to year. It's implied that twelve is an unusually high number of O.W.L.s.
See also essay on the number twelve.
Exceptional character moments
Mr. Borgin, speaking his mind once Lucius Malfoy is out of earshot.
Lucius Malfoy, who seems a far cry from the kind of father who could be bullied into giving Draco a racing broom (compare with Draco's remarks the previous year). To his credit, he's interested in seeing Draco improve his academic performance rather than, say, attempting to sabotage Hermione's to make Draco look better in comparison.
I've been really worried and if Harry is all right, will you please let me know at once, but perhaps it would be better if you used a different owl, because I think another delivery might finish your one off.
"Oh, it's you," said Ron, looking at Malfoy as if he were something unpleasant on the sole of his shoe.