Let's assume we not only encourage, but require students to use Wikipedia. If a student only finds factual information, then we've preserved the status quo, and nothing really changes. But what if the student finds a mistake? (Or, more likely, you find it for them.) This isn't a crisis, this is an opportunity! First, students see this as a powerful example of why we cite our sources, an idea with which many students struggle. Without the citation the student looks like they're wrong; with the citation to Wikipedia, we can see the student is not really at fault. Second, if a student finds an error in Wikipedia, don't ignore it, FIX IT! The same reason you cite as Wikipedia's weakness is also its greatest strength. Everyone can be an editor. Even if you just find a Wikipedia claim to be in question, and aren't sure if it's false, teach your students how to use the discussion page so they can truly take part in the Wikipedia experience.
If having your students participate as Wikipedia contributors sounds too scary, too involved, or not worth your time and effort, think of this absurdity you have created for yourself - You are a teacher, someone who dedicates themselves to helping students learn and share information, but you don't want your students to use your instruction in a way that contributes to the world's body of knowledge in one of the internet's biggest projects.
Like it or not, this is the world we live in, so put down your guard and teach your students (and yourself, if necessary) what digital citizenry can and should be about. In fact, you should hope all your students find mistakes in Wikipedia. Teach them how to fix those mistakes, and you can be sure "research" will mean more to them than churning out double-spaced papers.