He [...] nervously begins to scale the faces of the buildings. (11-13)
The Man-Moth clearly has some level of scruples, since scaling the face of buildings should definitely conjure up some anxiety.
He trembles, but he must investigate as high as he can climb. (16)
Folks don't usually tremble if they're just a little scared. This is bone-deep terror, and having no choice but to do it isn't helping much.
he climbs fearfully, thinking that this time he will manage (19)
What is he fearful of here? The task or succeeding at it?
But what the Man-Moth fears most he must do, although he fails, of course, and falls back scared but quite unhurt. (23-24)
What do you mean "of course" he fails? The Man-Moth doesn't strike us as a glass-half-full kind of moth, so why would he feel that his failure is inevitable? Does he not really want to reach his goal?
[...] He flits, he flutters, and cannot get aboard the silent trains fast enough to suit him. (26-28)
The Man-Moth's chaotic frenzy creates quite a ruckus since he's flittering and fluttering—which are rather noisy words—in comparison to the silent trains. Perhaps the silence of the trains is soothing to him, allowing him to chill out after his fall.
[...] He does not dare look out the window, (36)
Just like he knows not to watch ghost videos on the internet when he's alone in the house at night, the Man-Moth is not a thrill-seeker. He probably doesn't go to haunted houses at Halloween either.