A student posted a question on the SE site for writing. Paraphrasing: I was taught not to use Wikipedia for research because anybody can post anything, so I've been using a reputable published encyclopedia instead. But isn't stuff on Wikipedia reviewed? Is it trustworthy?

I answered:

Wikipedia is a crowd-sourced site where anybody can contribute, like Stack Exchange. Wikipedia strives for verifiability and neutrality and has an active user community, but that doesn't mean that things can't get past it. It doesn't mean information there can't be wrong. Some pages are full of detailed, reliable information; some are not. So, in evaluating the reliability of what you read on any given page there -- or anywhere else! -- you need to ask yourself how they know what they say.

Do they cite sources? Good Wikipedia pages do. Do they not cite sources but make a logical argument? (Not so common on Wikipedia, but common elsewhere on the Internet.) Do they present evidence?

Since you asked about Wikipedia I'll focus on sources. For a first approximation, ask yourself if the sources cited are generally considered to be credible. If they cite peer-reviewed, publicly-available research, that's pretty good. If they cite the National Enquirer (a tabloid full of sensationalist fiction masquerading as news), be very suspicious. If the facts you're checking are particularly important, central to your thesis for example, then you might need to actually go look up some of those sources to confirm that the Wikipedia page accurately represents them. If the facts are less important or tangential, or your assignment doesn't call for this degree of rigor, then establishing that Wikipedia's sources are credible might suffice without looking them up.

I wrote more about evaluating sources in this answer, drawing in part from this article from UC Berkeley.

For Wikipedia in particular, you can also check the "talk" page associated with the topic you're looking at. The "talk" pages can sometimes tell you if any content is disputed or of questionable quality. If the "talk" page is empty, though, don't assume that means everything's fine -- it might mean that no experts have looked at the topic yet.

It's impossible to say, globally, "Wikipedia is trustworthy" or "Wikipedia is not trustworthy". Unlike an edited, curated encyclopedia, it contains material at a range of quality levels. I find Wikipedia to be a good starting point in research; sometimes I find everything I need there (including supporting sources), and sometimes I don't. Don't rule it out, but do be prepared to go beyond it.