The main issue I have is an irrelevant ad plastered across every page would be pretty tacky. Having relevant ads on article pages would work better but there are a few problems with that:

a) Each article isn't of equal value in terms of advertising, which would make pricing much more complicated, which would also increase costs involved.

b) Pages (or whole topics) with rented ad space could be subject to spammy tactics to increase the amount of visitors, such as dubious SEO techniques (the Wikipedia domain would make this easy). I haven't thought about this deeply enough but it could be a huge problem since it can't really be controlled.