But doesn't anyone have a problem with an encyclopedia with articles written by anyone?
Sure, lots of people do. It's one of the primary criticisms leveled against open wiki sites. As such, it is covered extensively in
a Wikipedia article, which I suggest you read since the rest of this post will likely read like a condensed version.
How factually accurate are these entries?
Generally, it's expected that the more non-confrontational interest there is in an article, the more accurate it is. Obscure articles and those that are the subject of debate often contain incomplete, biased, or completely bogus information due to lack of interest, edit wars, trolls, and other issues.
Is there a screening system for this sort of thing?
Not as such, no. It's part of the Wiki mentality. As I understand it, some articles are protected if there is a problem with that specific article, and users can be banned if they repeatedly make edits judged to be harmful, but in general anyone can edit any article.
Someone could put in completely bogus info on a subject and no one would be the wiser.
No one, that is, except those who know the truth. The same is true of any information source, be it a website, a "real encyclopedia", a television show, a newspaper, a government official, etc. Although the wiki model has the disadvantage that anyone can introduce faulty information, it also allows anyone who knows the truth to introduce correct information. Ideally Wikipedia and similar sites could incorporate something like a "web of trust" mechanism and allow proofreaders to screen revisions, but their servers are loaded enough as it is. Really, though, this concern should continually be present regarding all media, not just the newfangled Internet stuff. You could say that a prestigous publication like the Encyclopedia Britannica is trustworthy, but do you really know that any more than you do with Wikipedia? Even if the editors and contributors are honest and generally competent, they could themselves rely on bogus sources or otherwise make mistakes...