Often there are many ways that changes are communicated (for example, an email to the NOC team to advise of systems being decommissioned, an email to the helpdesk to advise of new support procedures, etc). To some people, that email is the documentation. I know that if I want it captured in the knowledge base, that email is my cue to transpose the notification email into documentation that can be referenced later.
My current job is doing sysadmin support for a consultancy, so there are lots of clients and lots of other people doing this work. We have a regular pager rotation for emergencies, so if you get an overnight call to work on something and can't find the information about it, you start to realize how important the docs are. That has been a big motivator in getting people to update docs about the things they know. If you don't want a call overnight, make sure there's nothing that isn't in the wiki!
I use plugins to help point out when content might be out of date, and guide people to archiving out-of-date docs, or to update them. I regularly refer to Stewart Mader's great book Wikipatterns and its list of patterns/anti-patterns to help with wiki adoption and behavior. http://stewartmader.com/wikipatterns/ The book is a great read and covers a lot of your questions, especially skeptics and opponents, and how to address them.