Mandrake tends to run "cutting edge" with package selections. It's performance-oriented distribution, as opposed to a stability-oriented distribution, generally speaking. That's not to say that you can't run a stable Mandrake server, of course, or even a mandrake desktop, but it takes more micro-managing of package selection to get to that point. It also doesn't keep its URPMI repositories as carefully segregated as Debian does its apt repositories and Fedora its atp/YUM repositories.
Mandrake has been plagued with some high-profile stability issues in recent years. One glaring example was what happened to dual-boots when the 2.6 kernel was first introduced to Mandrake. Mandrake uses parted for partitioning and GRUB for its bootloader, by default. Combined with BIOSes on a large selection of motherboards that were mildly "buggy", there were some extreme conflicts arising between parted, the BIOS, GRUB, and the 2.6 kernel in Mandrake. As a result, many machines ended up with their boot sectors blued, screwed, and tattooed when attempting to set up a dual-boot with Windows and Mandrake.
Unfortunately, no, I don't have any proprietary software package names handy for you. It only takes a quick glance through the licenses for Mandrake installs to see where this comes up, though. It's not as bad as Linspire in this regard, but it does suffer a bit.
Your characterization of Mandrake as "one of the most open" may or may not be accurate, depending on your definition of "open". According to the Debian definition, however, it is not very "open". Fedora has moved more in an open-source-only direction than many competitors, including Mandrake. Gentoo has been basically all open source all along (necessarily, since it uses compile prepared "ports" rather than binary packages as its primary software management model). Then, of course, there's Slackware.
I have to wonder what you mean by "open" if it doesn't end up with all of the above in front of it in line for that label.
Unfortunately, I can't really comment on either Openwall or Annvix. I don't really know anything about them. I do, however, know that new distributions that are built on the model of another distribution end up often being less like the originating distro than some other distributions. Knoppix, for instance, is Debian-based, but in some ways reminds me strongly of SuSE. Progeny Debian actually feels pretty much exactly like Fedora. Heck, Xandros (which is also supposedly based on Debian -- a lot of distros are) looks, acts, and feels more like Windows XP than Debian in a lot of ways.
There's a GNUStep distro built on Debian that looks like the now defunct NeXTStep/OpenSTEP operating systems, and Debian HURD is just freakish. Then again, HURD is a modular kernel completely separate from the Linux monolithic kernel, so I'm not entirely certain that counts.
Anyhow, a distribution "based on" Mandrake may well make for a great server, but I'm sure its success in that regard has little or nothing to do with the Mandrake lineage.
While niche distros like that are often great for "toy" servers -- one-man pet projects -- they aren't really ideal for production environments in medium-sized WANs, or really in almost any business environment. The reason for that is simply that without as strong a corporate or community support network and diligent development-team crew maintaining patch distribution and testing for the distribution, eventually all such niche distros that don't explode into community stardom are pretty much doomed to fall behind on package (or port, or tarball) management. From what you say, it sounds like Openwall might not suffer that failure of niche distros, but I'd characterize that as an exception instead of a rule -- and that's assuming a lot of success, present and future, about Openwall based solely on the tenor of your discussion of it.
Generally, I'd expand your characterization of using the server also as a desktop as being likely to get you in trouble so that it also encompasses installing a graphical user environment on a server. The vast increase in potential security and stability issues, as well as greatly increased resource footprint, is just Not Good in a server. When you consider that servers simply don't need to have a GUI at all anyway, it's sort of a no-brainer to make the right decision.
Anyhow, that's my take. Your mileage may vary.
