How to share problem solving knowledge in a multiteam group?

Question

I've been working in multiteam groups for as long as I've been a web developer, and in my experience, a team can be a lonely soldier or several people; generally a company will have multiple teams working on different projects and once the project is out in the wild, any team can perform maintenance on it.

This is a simple example since I'm not talking only about project related knowledge, but "craft related" knowledge, but it should give you an idea of how I'm used to working:

Since we work on modularised teams, sometimes I feel like the teams are too tightly focused in their projects. I've seen cases where after an hour of discussion, the question was asked aloud and someone on a totally unrelated project suggested a much simpler solution.

The problem is difficult to solve because people tend not to be available all the time, and sometimes the person with the knowledge can't afford the time to go through a problem with the asker, but could do it themselves easily.

I've thought about software based solutions, something along the lines of SE, but I'd like to know other programmers opinions on the subject.

EDIT

I don't know if this is a problem that a wiki can solve, because I feel that wikis don't encourage the user to actually ask questions, but rather to write articles, and sometimes we don't know the knowledge we need before needing it.