A lot of the general public "knows" about Wikipedia, and knows that "anyone can edit it, so it MUST be wrong." Printed academic volumes are "wrong" in that they have errors as well (and often include errata sheets, even when first published), so the question then becomes "how wrong?" But even that isn't as important as public perception. Wikipedia is as good as many other online resources (even some for-pay resources) for research, but using references to it can give a bad impression. (Ref:
http://www.absolutewrite.com/forums/showthread.php?t=262579).
Did you notice the way it was cited? The important point is the date it was added. Whether it remains there a year or two later is irrelevant. The standard way to deal with the problem of web pages changing is to add "(accessed January 12, 2013)" or whatever date to the citation. For a claim like my hypothetical one that challenges conventional wisdom, I'd expect the author to have a saved screenshot or other evidence also, in case she was challenged on it.
I'd expect the author to know how to access the page as it was. Nothing is deleted in Wikipedia - when an edit is made, the previous version becomes part of the history and is easily available.
So your doctoral candidate brings a screenshot of a now-gone Wikipedia page to his defense? He/she will be laughed out of the building and sent back to McDonald's.
The OP was asking about the general public, but even so, I'd hope for something better than a screenshot of a no-longer-existing Internet webpage as evidence, whether from Wikipedia or not.
But again, much stuff stays online, and a smart researcher knows how to get to it. Here's a vandalized Wikipedia webpage:
http://en.wikipedia.org/w/index.php?title=Stanton_Peele&direction=next&oldid=68260725
and immediately after a revert to the earlier version was done (yes, I did the revert):
http://en.wikipedia.org/w/index.php?title=Stanton_Peele&direction=next&oldid=74933397
Many other (non-Wikipedia) webpages are saved online and are available years after they have been deleted, such as ordinary personal websites:
http://wayback.archive.org/web/20050415084832/http://www.mindspring.com/~benbradley/
...
If you want to refer to the actual population of African elephants in the world, you would cite some official source of elephant research. If you want to refer to the power of popular culture and the way different electronic mediums are becoming interconnected, you would cite the Wikipedia page on African elephants that showed the grossly inaccurate numbers after Stephen Colbert encouraged people to modify them. You aren't using the reference to show anything about elephants, merely something about Wikipedia.
You could also show how fast and how frequently such edits get reverted by regular Wikipedia editors who care that it is correct. Errors (and the inclusion of urban legends as fact) in print bppks only get corrected years later in later printed editions, leaving the earlier editions intact and (too) easily available, whereas popular Wikipedia articles have editors who get email notifications of every change of the articles they're tracking, and who revert vandalism within minutes.
If you're going to use Wikipedia for anything "important," or something looks odd on the article page, it's easy enough to (in addition to doing OTHER, independent research!) click "View History" and see who changed what, and (if they're good enough to leave a comment, which they SHOULD be) why. If it has an edit every few days or months, but then has dozens of edits in the last day, then you know something like the "Colbert mention" is up.
But to the OP, go ahead and use Wikipedia, but site the original source referenced in the Wikipedia article. A smart (arse) person like me might read your articles, look things up and see what you're doing, but most people wouldn't have a clue.