I applied for my APRC with a colleague at Zhonghe immigration office. (Ms. Bonnie Chung, #329)
Everything went smoothly and it took only 30 minutes for each of us. I would like to note some stuff that we might overlook (I overlooked some stuff).
Make an appointment beforehand.
I cannot emphasize this enough. The officer is loaded beyond her capacity since the regulation was relaxed. Call her and make an appointment so that she can (1) Check if you are eligible (2) Print out your entry/exit record and other basic information and (3) Might be able to check if you need to obtain your home country's police record and run medical check or not.
The officer at Zhonghe might be the nicest person on earth, but it looked as if she was on the verge of collapse, searching for a reason to explode. And yet she is the last person you want that to happen. If you feel like screwing things up for a stupid reason, such as getting upset for being told to go back and prepare this or that, remember it isn't personal, or there are other applicants waiting in line. Make sure you have done whatever you can. Why not start by reading every thread in this forum?
Copy everything in A4 size.
That applies for anything: work permit, passport, ARC. Otherwise the officer will do it herself, while you are left sitting like a scolded child, holding wasted papers and twenty minutes of your effort.
Copy AND sign the passport.
You need to copy the basic information page and pages/papers with Taiwanese stamps. Sign your name in the bottom corner on every page. Otherwise the officer will make you look (and feel) like Bart in the opening sequence of The Simpsons.
P.S. Actually it is not just about the passport - all copied documents need to be signed. In A4 paper.
It will (probably) take longer than the official 3 weeks.
The officer explained that all applications will be sent to a place in Taipei and will be processed by seven government personnel. (Of course it has to be seven.) The catch, again of course, is that not all of them are efficient (she actually said this). That's why the actual processing time varies. Good luck to all of us.
The bad news is that they are busy, and the good news is that they are busy. (Haven't we all done minor "incidents" during our stay in Taiwan? I don't think they have enough time to dig up the archives and decipher our past.) Good luck, and thank you very much everybody for generously posting information on APRC, especially Northcoast Surfer. I will post when I actually get the card.