Having stirred up a cloud of dust, Sophie has to sprinkle water in order to “lay” it.  I seem to have had heard of this practice before; I’m not sure, though. It would be like the first rain of autumn clearing the haze of dust and ag particles that follows the harvest. It makes the air fresh and the sky blue, but all I can see it doing to a stone floor is coating it with dirt that is now damp and slimy.
This leads to more sweeping, which also allows Sophie to sweep her way to the door so she can examine the fourth side of the knob and have a go at the cobwebby beams. Calcifer has been sneezing purple sparks since page 62. (The physiology of this is not explained.)
Marvelously spruced up, Howl enters.
He took one look and backed into the bathroom again with a blue-and-silver sleeve protecting his head.
“Stop it woman!” he said. “Leave those poor spiders alone!” 
The ensuing conversation is not so much about spiders as about boundaries. Howl may regard Sophie’s response to them as a test of her Witch of the Waste credentials or lack thereof: even those of us who dislike spiders, and are terrified of turning over a planter or a board and finding a black widow, would prefer to let them be than outright kill them (at least I would). If Sophie can remove the webs without harming the spiders, that will ease some of his misgivings about her real identity.
On the other hand, he’s got a real infestation there, which enhances the creepy-castle air of the place. Likewise, the spiders represent another object onto which Sophie can project the anxiety of her unrealized feelings about Howl: “Probably he had a wicked affinity for spiders, Sophie thought.”
Either way, the subject is changed from their mutual efforts to impress one another. The boundary-crashing continues, however:
Sophie leaned on the broom and watched Howl cross the room and pick up his guitar. As he put his hand on the door latch, she said, “If the red blob leads to Kingsbury and the blue blob goes to Porthaven, where does the black blob take you?”
“What a nosy old woman you are!” said Howl. “That leads to my private bolt hole and you are not being told where it is.” He opened the door [green-down] onto the wide, moving moorland and the hills. 
“Bolt hole” is a British phrase that apparently means “escape hatch.” Actually this seems to go for any of the castle’s exits, not just the black one: Howl walks away from the entire situation, leaving Sophie duly warned about spiders, Michael “despairingly” wondering when he’ll be back, and Calcifer crackling “with malicious laughter.”  When you’re a slitherer-outer, any old portal will do.