Great thread. Thanks for starting it.
I have a bit of experience with several different "Living" campaigns, and "improve" is a tough concept, because one person's improvement is another's rant-inducing, flame-provoking cry of "you killed my campaign." I would say that rather than thinking of improving, a discussion of the different poles of organization and design would be beneficial.
To start, I think it is best of remember that "Living" first meant something different than it does today. When you went to conventions to play sanctioned tournaments back in the day, you were given a pre-generated character, and when the tournament (whether one round or several) ended, that was the end. Living City was created as an alternative to that, where you could bring your own character, gain treasure and experience, and continue playing that character at subsequent events. Also, you could have those characters interact with other characters in different ways: trading or selling goods, for example. Certainly the whole "characters affect their environment through game play" was part of the selling point, but it wasn't the only aspect, and probably wasn't even the major selling point. We've come so far with these types of campaigns that it is easy to forgot just how revolutionary the idea of bringing your own character to a tournament and advancing that character actually was.
Now in terms of if and how a Living Campaign allows character actions to affect the ongoing story, in the campaigns I was involved in, it happened many times and in diverse ways. Sometimes it was done through tabulating results provided online (like we did when people reported their results in WotC's Eberron-based Xendrik Expeditions campaign. In the faction of that campaign I oversaw, a potentially major NPC was not rescued in one adventure by a majority of the tables, so he did not appear in later adventures, and the plot I had planned changed because of it.
In Living Greyhawk, many changes were made in the overall plot of different regions based on events that were either tabulated through reporting, or were based on the results of what became known as "interactives." These were large events that saw many tables of players going through the same adventure (or linked adventures) at the same time. Not only did the outcomes of these events change the course of plots and settings, but often the various players got to interact with each other. Think of the defense of a city where each table of players was in charge of defending a different section. Groups could assist each other, send each other information, etc.
The main factor that determines how much player-driven results can change the plot and setting of the campaign is the size and scope of the campaign setting. Trying to change the Forgotten Realms is a bit tricky, since there are currently probably 30 different RPG, novel, board game, computer game, and lunch box design or development projects taking place there. The Living campaign staff isn't going to just shoot an email to someone at WotC and say, "Oh, by the way, Szass Tam is dead now. Tell all those novelists and game designers that his cousin Bernie is now ruler of Thay."
Organizations with more granular control over their settings, or who make their "Living" campaign a larger focus of the setting, can go much further in giving the individual players a chance to impact the world through play. But even then, all of the issues of timing, adventure availability, production lead times, and other fidgety details rear their ugly heads.
I am not as familiar with Living-style campaigns for non-D&D campaigns, so I would love to hear other examples about how some of those other campaigns may have been different from my experiences.