I like the show quite a lot. He makes mistakes, but the show is pretty good at following up with them and exploring the errors (for example, Byrne realized he was being ham handed after the Laura attempted-termination episode and recognized that he had clumsily made use of supervision--patients are very good at picking up on comments that don't ring true but which reflect a parroting of somebody else's views).
I agree about the soap opera thing: if Alex and Laura have some wild thing, it seems to me the writers are working too hard (or maybe working too little and falling back on sensationalism).
Nevertheless, I really like the way that Byrne appears to be thinking about unconscious behaviors while not simply following the usual interpersonal pleasantries. He makes use of the transference in looking for patterns and is curious about his own countertransference. The latter is one reason that people who intend to become therapists should (my opinion) go into therapy themselves. I haven't seen evidence that Byrne is an analyst, though he does use analytic techniques, and his expertise hints at another of my opinions: a psych residency prepares people to learn how to become therapists; to become an expert therapist, you have to be a genius at therapy (I haven't met one yet) or get extended supervision or training (as in ongoing therapy classes or analytic trg). The lifelong aspect of learning is crucial; the typical go-to-an-office-and-sit-there-for-30-years is one important reason that therapists become jaded.
I appreciated his focus on evidence within the room rather than some sort of "let's look at your childhood" thing. I like the way that he handles gifts and sexual overtures differently, depending on who is offering, and when. And I like the fact that his personal life is screwed up, that he is something of a mess in his own therapy/supervision, but that he maintains curiosity and passion.
Again, a little sensationalistic--how many affairs and miscarriages and sexual abuse can you compress into a couple of weeks--but I've seen all of those behaviors within a week, including stuff that would be too unpleasantly detailed for tv, and they do have to make it interesting for ratings. Anyway, I think it's the best representationof psychiatry/psychology that I've seen on the screen.