I am a very fast editor and writer.
Now to the his or her vs. their issue. The problem with "his or her" is that although it is certainly more inclusive than "his," which folks used to use as a default, it is still not entirely inclusive. It references only those who are firmly on one side or another of the gender binary. I have non-binary friends, and I know how much they appreciate not being excluded, and how hurt they are by being routinely excluded.