|Perl Monk, Perl Meditation|
Well . . . I'm the guy who first mentioned the "trilogy" in that FreeBSD thread. I pointed out that the traditional camelid trilogy is the Llama (Learning Perl), the Alpaca (originally Learning Perl Objects, References, and Modules, and now Intermediate Perl), and the Camel (Programming Perl). I also mentioned that the Vicuņa (Mastering Perl) is now available, but since I haven't read it I can't really comment with any authority on its value.
While I'm sure Advanced Perl Programming is kind of a must-read (I've skimmed, but not really had a chance to read, the black leopard), it seems to me like something to get after those I mentioned above. Since I haven't read the Vicuņa, and haven't read APP in any depth, I can't really say whether one is a better follow-up to other books than the other, though. I'm just pretty strongly of the opinion that the Llama and Alpaca are an awesome first and second book for an introduction to programming with Perl, and practical competence requires a good reference with explanations on the shelf.
I think your question implies that there can only be three must-read books for Perl. I don't really agree with such an assumption, though. I think it's perfectly reasonable to talk about a camelid trilogy, and to just say "Perl Best Practices and Advanced Perl Programming are also must-read books if you're serious about being a Perl programmer."
I'm not so sure Mastering Regular Expressions is a must-read for Perl programmers, exactly. As far as I'm aware, it's not even a Perl book, per se. I'm sure it's a great book (though I haven't read it), but that's not the same thing as being a must-have, must-read Perl book (especially since not all Perl programming requires regular expressions, though of course one needs some competence with regular expressions to be a truly competent Perlist in my opinion).
Anyway, I guess that pretty much sums up my opinion on the matter. I reserve the right to change my mind if and when I get around to reading some of the books discussed here that I haven't yet read.