Panel 1: where we see Dan getting yet another new lock from the Gordian Knot Lock Company, for his apartment, to replace the one that Rorschach broke at the end of Chapter III (which itself was a replacement earlier in that same third chapter for the lock Rorschach busted in Chapter I)
Detective Steven Fine, as identified (sans first name) in the back-matter for Chapter VI, is one of the detectives working the Eddie Blake murder.
Panel 3: Note the owl on the calendar that Detective Fine is looking at in the background, an obvious visual metaphor for Dan’s alter-ego.
Panel 5: All of Detective Fine’s remarks and questions are meant to clue Dan in that the detective knows he is Nite Owl, including his offer of a cigarette to Dan. Significantly, Dan tells the detective that he doesn’t smoke – the importance of this statement made more obvious in just a few panels.
Also, Detective Fine no doubt already did a little research on Dan and knows that he lives alone. The two coffee mugs would be a tip off to him that someone relatively new is living there, whom he most likely suspects is Laurie Juspeczyk, the Silk Spectre.
Some bits of visual minutiae – Another headline about the increasing hostilities on the Eurasian continent as tanks mass in Eastern Europe, close to Afghanistan and Pakistan.
Note that Governor [Ronald] Reagan (who was actually President at the time, but obviously could not be if Nixon had achieved his five terms) is urging a hard line on these hostilities, which can certainly be taken as a remark on Reagan’s Presidential policies of the time, especially his hard-line stance against the USSR.
There’s the Nova Express issue with the “Spirit of ‘77” theme, as noted by Bernie the newsvendor earlier in this chapter.
The bag of sugar on the counter is new, a result of Rorschach’s first visit to Dan in this book.
Panel 6: Detective Fine would have also noted the two coats hanging on the hooks as he entered, visible in this image.
Also note that the new lock shines quite brightly – an ironic visual statement possibly, considering how easily similar locks have been breached earlier in the story. And the manner in which those locks have been breached is similar to the manner in which the riddle of the Gordian Knot from ancient times was solved, through lateral thinking and brute force.