Successfully managing a project is often a difficult task. Mixing deadlines, a limited amount of time, money & people to achieve loosely defined stuff make a good recipe for disaster. Here is how a wiki might help you minimize the bill.
One of the recurrent problems of having a project spanning various corporate boundaries (between teams & deparments for instance) is that stuff happens in many different places (mailboxes, Enterprise IM, phone, shared drives...). With a wiki, you can have everybody adding their stuff to a central place where it can be organized through links & tags and be made available to all the people involved.
Keep Track of What's Happening
Every business wiki has a built-in notification feature, be it through RSS, email, dedicated pages or many of them at once. You can use this feature to stay up-to-date on who's contributing what & when they're doing it. Thanks to this, you won't have people arguing on whether or not the mail they were supposed to send ever arrived on time: if it's not on the wiki, it isn't there. Productivity seldom accommodates nitpickyness.
Share & Organize
Wiki pages are a great place to jot down every kind of information, ranging from a PDF or a MS Word file to a plain old scanned paper-note. Most search tools nowadays will be able to search into the content of pages & text attachments and rank the results to provide you with an effective way to access information. Even when loosely classified, the data you need will remain available on your wiki.
So mastering project management sounds good to you... what are you waiting to try and go wiki?