A few comments on the article 
Good article overall, but in reading through it I think that certain areas are in need of improvement. Firstly I thought there wasn't really enough explanation of why it would be preferable to build a Space elevator. The economics section has info on costs and all, but this is rather brief and comes towards the end of the article, I would think that explaining the perceived necessity of such a device would be one of the first things to state.
There were some things about the specifics of the engineering which I think need a lot more explaining, for one, is it proposed that the cable be a single thick wire or many tiny thin ones? It seems to be talked about at various points as if it could be either, so I think that needs more clarity.
Something quite important that I don't think was addressed at all (or at-least I couldn't see it) was the issue of how exactly the cable (or the whole structure) actually gets up into space in the first place. Are we to assume that the cable will be towed up by a rocket or something? If not that, then how?
Several times in the article it is mentioned that the "Counterweight", could be an asteroid or a space station. But these two things are very different aren't they? I mean in terms of mass, an asteroid probably weighs millions if not billions of tons, whereas a manmade space stations would be only a few hundred or thousand tons (unless some gargantuan station is proposed). So how can these to things be comparable? And what kind of actual weights will be involved?
Finally the article doesn't give much information on how the climbers are proposed to move. It is mentioned further down that Magnetic levitation might be used, but is that the norm, is that what they all propose? Or are there different plans, like just mechanical wheels, etc?
Well that's about all I can think of for now, I hope the article can be improved with some of these suggestions.