Why does the author leave it unclear whether Goodman Brown's experience is a dream or real?How is this noted in the story or what does the author...

It does matter that Hawthorne leaves it in ambiguity.
Hawthorne leaves it up to the reader to decide. Let’s say it was real. Brown went into
the woods and learned that all those he thought were pious and religiously devout were
actually hypocrites: as full of sin as anyone. It was like a nightmare. It completely
changed the way he looked at his community. This changed his outlook on faith and
life.

Let’s say he dreamt this. It was such a powerful
dream that it changed the way he thought about the world. The dream introduced doubt
that he never before considered. A dream is an abstract thought process. Although it
occurred at night, it could have been more like a daydream: a more consciously directed
conception of things. If this dream, daydream or serious contemplation was powerful
enough, it could also change the way Brown thinks about the world and thereby, the way
he acts in the world.

Either scenario works. One is an
actual physical experience that changes him. The other is a mental realization. Brown’s
problem is that he cannot reconcile the fact that good people are fallible. He also
cannot forgive the ultra-religious for being so hypocritical. So, he’s being
unreasonable but also astute in his observation of those who preach but do not
practice.

In either case, Brown has metaphorically and then
literally lost his faith. The obvious pun is on his wife’s name. In losing his faith, by
dream or reality or thought, he loses his trust and connection with others. This
includes Faith.

Brown cannot accept the good/bad duality of
human nature. Thematically or formalistically, this story also has an inescapable
duality. We don’t know if it is a dream or if it is real. Potentially, it could be both.
The story itself is an inescapable duality.