In response to your first two (similar =) points, I think that a section like this would be valuable in fighting the Golf problem you mention. With other kinds of challenges around, competetive spirit could be used to foster better code writing. Challenges needn't be limited to writing short (bad) code. Writing readable or portable code is often more difficult. Different things are learned from each.
I can see the advantages of a list like Quiz Of The Week, but not just anyone can post to it. That's very key to the goals I have in mind. An important one to me is that theoretical questions somebody actually needs answered could be dealt with, but in an enviroment which lays emphasis on the fun of the challenge. Anybody ought to be able to post, and like every other section, I think posts should be approved and moderated by people who have those abilities based on their level. The standards of what is acceptable would by necessity be different from the others. Standards should be more strict than SoPW, in my opinion, but since judging wouldn't be a terribly formal procedure (see below) it's not something I'm extremely concerned with. Heck... a challenge to write a good challenge (with guidelines as to what that means) would make a good first post to the section.
(Just as a side note, I could accept an argument that posting challenges should be limited to a certain level, like in Q&A, and for many of the same reasons.)
As for the quality of responses, those who use and test them would respond based on all the criteria they find important. Encouraging people to take speed, readability, and other qualities into account is something I hope would be encouraged, but everybody has their own idea of what's important, and not all of them match mine. Partly for that reason, the judging system I was envisioning is PM's own voting system. Those who think a particular answer is a good one for the question vote it up. Those who think otherwise abstain or vote down. The "first post" problem is one which probably won't be solved, but which would hopefully at least take a hit from the fact that answers are expected to match the question's criteria, and thus will be more carefully scrutinized. If speed isn't important to the poster, it needn't necessarily be important in the response. If it is, it should be. And for well defined challenges, the first post problem disappears.
As for adding the new section, I'm not in pmdev, but I'd really like to see this happen. If the idea has general approval, I'm willing to do what's needed to make it happen, as much as is within my ability. If profuse help is going to be necessary (I have very little idea what's involved), perhaps somebody capable will be willing to help me.
Update: PS: I forgot to mention, but I do intend to put down a specification for this if it seems like it might happen. I already have one in my head (actually two or three possibilities) and they've changed a little as I read your response. Maybe in a day or two I'll post them, when I've heard more people's opinion and had time to think more.
Love justice; desire mercy.