Here is a list of things, I would consider important to me if I was to judge a contest such as this:
1) Mood. Does the story fit the ages general feel. This is a very subjective idea, but also it is very important when creating a story of a place that already exists. You need to find the essence of the place, and find the reasons why it is as it is within the story. Sometimes a writer can get wrapped up in a story they want to tell and thus lose sight of the general feeling of the age itself.
2) Characters. Are they well crafted? Do they accent the age, or distract from it? Any character needs to be fleshed out properly. It doesn't matter if they are fully described or even if you know much about them at all, but they need to have a personality and something that readers can connect with either in a good or bad way.
3) Flow. A story is more than just a list of events. It also shouldn't feel awkward or disjointed. Also it's best to not get long winded. If a story requires a lot of text to tell it, then that is OK, but try to avoid to many tangents or very long tangents that detract from the story as a whole.
4) intrigue or interest. Does the story grab me? Do I care about the characters? I need to have a reason to get to the end of a story. I am not saying that it should be a surprise, cause some of the most interesting stories I have read were based on true events which I knew the outcome. What you need is to make the story intriguing enough that I must finish the whole thing to understand it all.
5) (this is specifically for this contest) Accuracy to canon. Though there is a lot of license in age writing to create whatever you wish, your going to be working on something that exists already. Not to mention that you would be writing within the world of the D'ni and it would be best not to tread to harshly on their world. So it would be important to not make Ri'neref fly into the age and smite it with his eye lasers.
6) Believability or immersive aspect. Similar to the above, it is important to not write anything that breaks a persons immersion in the story. Like lets say you write a story about the nights of the round table. It would break many people's immersion if you suddenly decided that Galahad invented the silicon chip and created a robotic dragon to fight off his enemies. Unless of course you properly set up the story to cover that. Basically avoid plot holes. They cheapen the experience of any book, movie, or age.
That's about it. Just a reminder that this is what I would be looking at, not necessarily what should all be added as a guide for judges.
BTW, it would be interesting to use the one age idea that Bob put forth. Perhaps have that for this first contest and then step it up a notch next time by having writers and modelers team up per age?