Sure, I'll contribute to this. I started in my tenure-track faculty job (R1, but barely) right after internship, so there's that. I won't even go into the applying for faculty jobs, negotiating offers, etc., except to say that the gap between internship and the first job (whether post doc or otherwise) can hurt, financially speaking. I negotiated both moving expenses and a month of summer salary before I started so that I was continuously employed...that was a good idea.
Lets see, issues I've faced that seem specific to ECPs. As an academic, there is a lot of freedom...no advisor giving you deadlines, no clients you don't want to see....but that means you have to be really self-motivated. Getting a lab up and running is no joke, and unless you helped your advisor do that or were given specific training on how to do it, you're kind of flying blind. Relying on slightly older faculty can be useful, *if* they are willing to help, and *if* they remember.
Teaching can take over your life. I taught several courses in graduate school, so I knew this, but I always seem to underestimate how long teaching prep takes me, and how much more I feel I could be doing. Beyond prep, the actual teaching and the (ugh) grading is also ridiculously time consuming. Many faculty gigs will give a course release in the first year, but even so, it's a lot of work. Good time management helps wonders here. Also, there is research to suggest that students take advantage of faculty who look young/new and are female. I (am female, and look young) take the "hard ass at first" approach, where I look kind of mean (part of that is just my face, I have resting bitch face) and lay down very clear but strict expectations. It's much easier to start hard and get more lenient as the semester goes on than the other way around.
The other things I wanted to mention are supervision (broadly defined, including clinical supervision and research mentorship) and politics. Supervision, as was pointed out in the other thread, is a skill that can be learned, but most clinical psychologists don't get much training in supervision. We get even less in mentoring broadly. There are decisions to make: how many students do you want as RAs? What will you do for them, what will they do for you? Will you be mentoring graduate students? Should you take one right away, or wait? Those are the practical things....the other stuff (e.g., figuring out your supervision style, your values in mentoring...) these are amorphous. There's little oversight, so you can do whatever you want, but there's little guide on what "works" unless you happen to have a very good internal barometer and/or you are adept at eliciting (honest) feedback from your supervisees/mentees.
The politics are also interesting. As a graduate student, I didn't get much insight into the department politics of the faculty even though I tried to pay attention and I was involved with more administrative work than most grad students. As a faculty member, though, navigating those waters is tricky. Who has what beliefs? What are entrenched policies? Are there factions? What are the individual goals of the faculty members in terms of training at both the undergraduate and graduate levels? When do I, as a young faculty member without tenure, speak up? When do I stay silent? (Note: I mostly stayed silent in the first year, with a few exceptions).
A few other things: figuring out licensure, taking the EPPP while doing all of the other crap talked about above. Plus trying to do *some* service but stay away from too much service so it doesn't undermine all the other stuff.
In case this all sounds overwhelming, there ARE forums and stuff (Chronicle of Higher Education) to talk about these things, as some of these issues are not unique to psychology. And goodness do I *wish* there were a forum for talking about supervision!!!!! I should also point out that I wouldn't trade my job for anything, I love my work, and my department. But only now am I feeling like I have a handle on supervision and mentoring, and the politics piece remains a challenge. At this point, I know the politics and the personalities of my department, but not necessarily how I can and should contribute my perspective most effectively.