This post got more replies sooner than expected, so here goes -- I am the original bumper of this thread:
Did you clerk in a district court first?
When did you start looking for any clerkship at all?
I started thinking about it the spring of 2L year (maybe April-ish?) I started gathering my recommendations in late-May to apply to off-plan judges. If that helps.
Do your judges or other judges whose habits you can speak to consider LR a requirement?
Based purely on instinct, I think one judge does, the other does not. I will say that what you do with your LR position is much more important than whether you are on LR (e.g., have you been published?)
If LR isn't a requirement, is editorial board of your journal?
Same answer as above.
How many professors did use for recommendations?
Four, three at a time. By the time I applied for my second clerkship, I asked another professor who I felt knew my body of work better to write recommendation letters for me.
Did a professor make a phone call for you? Did more than one professor do so?
Yes. For clerkship #1, I asked one professor to make phone calls; for clerkship #2, two made phone calls (oddly enough, the judge I will be working for was not a contact of either professor, so I think there is still a lot to be said about being hired purely on the merits).
How did you start looking for clerkships - talking to professors, or your school's clerkship office, or looking on Oscar?
I started with my school's clerkship office, but, through no fault of our clerkship advisor, had to do a lot of legwork on my own. (We historically don't place a lot of graduates in Article III courts.) I spoke with professors, did my own research, figured out who might be able to contact which judges, etc.
How much work had you done with the professor who called for you - one class, two, RAing, all of the above, or more?
One or two classes.
In your clerkship interviews, how much attention did your writing sample get? What topics were the most commonly discussed - the judge's past opinions, your personal development, your published work?
A lot. I had five COA interviews, and during all but one of them my writing sample was brought up. The judge's past opinions less so, but I think for some of the more competitive COA clerkships, it would be helpful to show that you've done your homework and that you genuinely know who you would like to work for.
What advice do you think you would give someone who aspires to clerk for a Federal judge, either district or CoA or both, that you think would be non-obvious?
What things do you think you could have done to make your application, and your interview, stronger? What non-grade, non-LR distinctions do you think you had that got you picked over other applicants?
I'm going to take both questions as one and the same -- I think on top of grades, LR/journal, etc. (which are necessary but not sufficient), publication is a big factor for some COA judges. Courseload is another key factor for some COA judges -- they like to see that you've taken the heavy hitters and you've excelled. Finally, as a poster mentioned above, personality counts a lot -- by the time you are asked in for an interview, the judge has already figured that you've met the paper credential requirements.
In terms of things you have control over -- try to develop a rapport with two or three faculty members. Not just, "Oh, hello, can you write me a clerkship recommendation, I did well in your class!" -- but try to develop a genuine relationship with them. Drop by their office, ask them how they're doing, what they're working on in terms of scholarship, "How about that local sports team?" -- etc. Some faculty members are great people, and the more they get to know you personally, the more they will go to bat for you. Some profs, you won't be able to develop a connection with. But at the very least, give it a shot.