Should I accept the cite?
Her prompt was “What strains did the inflation of the 16th Century create for European governments, and how did they respond? Make sure you discuss a minimum of two countries in detail.”
Is Cecil a valid source? If it had been a Guest Column I would’ve rejected it out of hand, because some of those are written (or co-written) by idiots. But Unca Cece? Do I dare? 
Accept it? You should give her bonus points! (Though perhaps you should also ask her for a bio on ‘Cecil’ so she pays a bit more attention to her sources.)
Unca Cece has sources. I’m inclined to say maybe she should have cited those instead, but they’re not exactly net-friendly, from what I can recall.
Students in need of primary (or even secondary) sources have excellent access to libraries.
As much as I like Cecil, a newspaper weird-facts column is not an appropriate cite for a research paper.
Just out of curiosity, and for when my college bound kids eventually ask, what are the standards for citing internet sources? Back in the day, as long as the cite came out of some random book in the library, that was good enough. Nowadays, just because you find it on the internet doesn’t make it true. I guess not even Wikipedia can be considered a reliable source for some ( most? ) things. Do I tell them that the Straight Dope and Snopes are the only true sources on the internets?
Not even? Especially not, I’d say. No matter how reliable it is on average, it might as well have been the student who wrote the article she’s citing.
Did the student have other sources (especially ones that also address the topic in the SD article?) If it is her only source, then it isn’t enough and she should be marked down for it. If it was a starting point, or perhaps even referring only to one brief point she made, but the rest of her sources are satisfactory, then I think she should get full marks.
There is nothing wrong, IMHO, in using a source like the Straight Dope, or Wikipedia, or the World Book encyclopedias as long as they aren’t your only sources. I’m working on my second university degree, and when I have to write about something new, I always start with a general reference, to understand how to approach my topic and to figure out what key words I need to be researching for, and I have never been marked down for it (I do include it in my list of references).
ETA: I do, of course, do the rest of my research and cites from actual books/journals/etc.
Well, the best part is that reliable information on Wiki quite often has a direct link to an online version of the primary source.
Stuff in books is barely more accurate than the internet. Original research is the way to go if done right, otherwise just more garbage. How do you evaluate any source? You go to a number of sources. And since this is a secondary source paper, you are going to need what appear to the student to be three reliable sources or some such.
I’d be careful because it might be that the student heard you talk about the SDMB and is trying to kiss ass.
Treat it how you would any other newspaper columnist. For some papers that’s an appropriate source and for some papers it isn’t. David Brooks’ columns are online and are occasionally accompanied by strange commentary from internet denizens at large, too.
Also, using language in your paper that identifies the cite as an opinion or conjecture can clear up some (not all, of course) of the dubious cite questions. Then use the standard citation format for internet sources outlined by the APA or whichever guide your instructor prefers. This is if the tone and subject matter of the paper allow for it, such as persuasive essays.
“*It is the opinion of *<some guy on Wiki> that the blah blah was directly related to this other blah blah. <Cite>”
“Cecil Adams, of the Straight Dope, suggests that the cause of the blah blah in 1973 was influenced by previous events that occured surrounding blah blah in the sixties. <Cite>”
What level do you teach at?
If it were me, I’d give the kid bonus points, but I’m not a teacher.
In theory, I agree, though for many topics in history it’s pretty hard to go to the sources for a student paper (e.g. most 16th-century European history). Also, Cecil Adams isn’t just another secondary source for this kind of history - his column is based (presumably) entirely on other secondary sources. Plus, he’s not a historian. And I have prejudices about such things. 
In general, the main difference between books and the internet is peer-review, but I think the context provided by books is also important - I’m a bit wary of students googling “inflation 16th century spain” or something, and getting snippets of information from various websites. Of course, they can do this with indices of books as well, but it’s much better to read an entire chapter of a book, and draw out the important stuff.
When I took my Senior Thesis class our professor discouraged any sources on the internet unless they were a newspaper archive or a database such as JSTOR. In other classes internet sources were allowed to a point. We went over ways to determine an internet sources validity. Generally any site that ended with .edu was allowed. We were strongly discouraged from using Wikipedia, with one professor promising a grade no higher than a C if Wiki was used. One professor didn’t mind if we started our research on Wiki because as Santo stated there are links to other online sources.