These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Fridge Logic - The reason that in the beginning, female characters couldn't become diagnosticians. The in-series justification given by O'Mara early on is that females are more aggressive when it comes to mental defense than males. While male characters suffer a lot of discomfort from educator tapes imposing foreign feelings and thoughts on them, females will generally automatically destroy an educator-tape imposed personality that tries to tamper with them like that. Given the series' rules about psychic abilities, it makes sense for a species with latent psychic abilities that carries young to be able to ensure they don't take over or influence the parent's body (see the Protectors of the Unborn). This tallies with Conway's experiences with psychic contact, which generally (especially early on) consist of sudden infodumps that he doesn't have a lot of control over, while a female physician in another book is much more in control of her own psychic contact.
Bearing this out, while female educator tapes were taken, they're deemed unsafe by O'Mara and he would know. You have to wonder how much of O'Mara's not-exactly-romance plot is caused by the fact he's a Jerk with a Heart of Gold and how much is caused by letting a desperately unhappy personality that's much better at psychic warfare than he is into his head and being unable to get himself to remove it, even though he should know that's the safe and sane thing to do. The Fridge Horror turns a touching storyline into Nightmare Fuel.
Murchison later becoming a pathologist can be explained by Technology Marches On - the educator tape system has been improved and it's harder for a host's defenses to force out the foreign personality. While it doesn't say that she started using educator tapes, the attempted appendectomy in one of the books shows how important educator tapes are to interspecies medicine, and even if pathology doesn't involve living patients, it's still diagnosis and a physician without an educator tape would miss things that one with an educator tape would see. Since Sector General wouldn't stand for that kind of oversight, unless she can host educator tapes for at least short periods, it's doubtful she would ever have gotten the post, despite her experience and connections.
Inferred Holocaust - The Galaxy is peaceful and utopian because the only species moving around are the ones that grew past war and achieved the unity required to go stably interstellar. This may mean that the rest are still maturing, or it may not.
Earth-humans and Orligians, the first sentient species that Earth-humans made contact with, actually fought a war shortly after their First Contact. They're both very embarrassed about it.