Your questions are good ones, and as you saw, a good deal of what we did in class today fit in with the topics you raised. I even tried to be fair to Kant, who is not so bothersome as some of the people who followed him in the nineteenth century. I too would be concerned about the discovery of a non-orientable wormhole.
I hope that some of the discussion of the real projective plane cleared up some of the possible difficulties, although there are certainly a number that will remain--people have devoted courses and books to the subject after all. I emphasize the topological aspects in my own courses, so that is what shows up in the book.
And just in case someone else wonders about the misnumbering of my reference to a pair of planes meeting in one point in four-space, that error has been corrected in the second (paperback) edition. Thanks for noting it.