You'd think the inner dome of heaven had fallen. (Line 13)
In "Kubla Khan," the stately pleasure dome that Kubla Khan built collapses like an interrupted vision.
But I was going to say when Truth broke in (Line 21)
Like in Coleridge's "Kubla Kahn," the speaker's vision in "Birches" is interrupted by a strange visitor. This time, however, the visitor is "Truth," a concept that often sparks skepticism. How do you understand "Truth." Do you take it at face value? Do you understand it in an ironic light?
May no fate willfully misunderstand me (Line50)
Frost has thrown in "fate" another personification that can be as scrutinized as "Truth." But then again, you could also take these two concepts seriously. The poem doesn't necessarily argue that one interpretation is better than the other.
Toward heaven, till the tree could bear no more, (Line 56)
The image of the tree leading the speaker towards heaven may be intended to evoke Jacob's Ladder, a ladder that goes to heaven as described by Jacob in the book of Genesis.