One thing that comes to mind immediately is his third chapter on the Anima and Animus, which are perhaps a bit more reliant upon gender complementarity than necessary. I think the anima/animus are a helpful way of conceptualizing what Jung meant by the Shadow, but the language may prove somewhat distracting, especially 60 years later in an era more open to non-binary gender identities and sexual identities. Additionally, I personally don't see Christianity as the common mythos today that Jung believed it to be for the West in the 1960s; assuming he was correct in that assumption, or even that Christianity had been a unique space through which the "Western psyche" was working through its own psychological development, our own era seems both more diverse and far more post-Christian in this respect, so much so that it may be more viable to speak of Jung utilizing Christianity as a set of myths to express psychological ideas that could also be expressed through other myths (a still very Jungian take) rather than arguing that Christianity was the space in which the West articulated and experienced these ideas.

Of course, this is just my perspective. I'm certain others see it differently. My general approach to Jung, though, is as something of a post-Jungian: I value his work while also recognizing both that we live in a very different world than he did and that we have learned a great deal more in psychotherapy, neuroscience, and general psychology since his career.