Flannery uses his spyglass (this fancy-looking device) to spy on the ladies. Yep. He's kind of a creeper.
If we dig beyond the creepiness, though, this spyglass shows us how men try to gain a sense of power by staring at women as if they were objects. Sort of like the way you, the Reader, think of Ludmilla, right? Yeah, Calvino's consistent.
But why exactly is Flannery spying on this woman to begin with? Well, he wants to know what she's thinking. He has this kind of insane idea that she's reading what he's writing—while he's writing it:
"the sentence I am about to write [is] the one the woman is reading at that same moment. The idea mesmerizes me so much that I convince myself it is true: I write the sentence hastily, get up, go to the window, train my spyglass to check the effect of my sentence in her gaze." (15.4)
So his spyglass might even represent the anxiety that he—an author—feels over wanting to please his reader. Flannery's struggle is the struggle of the author trying to write ideal material for an ideal reader and to get an ideal response.
But in the end, Flannery admits that he often feels "the distance between my writing and her reading is unbridgeable" (15.5). There will always be a gap between writing and the perfection that it's aiming for; there are just too many variables involved in the movement of ideas from author-to-page-to-reader for everything to run perfectly.
But then again, why would Flannery even keep writing if he finally wrote the perfect book? For Calvino, it seems to be the endless failure of words that keeps writers writing.