In general with the comments on @EAMann's answer I agree with both @Jan and @Adam Backstrom; there shouldn't be a problem. The GPL's requirements are only triggered upon code distribution and since StackExchange is not distributing it's own code the GPL issue is really a moot point.
HOWEVER, and this is where it could get really interesting; the code that people write on StackExchange (like the code each of us have written when answering questions) could come under dispute. StackExchange is requiring all content we contribute to be licensed cc-by-sa and it doesn't appear that Creatives Commons is directly compatible with GPL (which pointed to a potentially even broader concern; more on that in a bit).
As all of us know Matt Mullenweg has taken made a very visible stand with regarding to the licensing of themes and plugins. Matt has asserted that themes and plugins are derivative works of WordPress and thus must be bound by GPL v2. If we take that on face value (more on that in a bit) then we have a situation where code distributed with a CC license much also be licensed via GPL, but the two are not compatible. What to do?
It gets worse. The code found on WordPress answers can now not be used in plugins or themes because, according to Matt, they must be GPL. But GPL is likely not compatible with CC. So we have a rock and a hard place.
Now the easy answer is to just have both the WordPress Foundation and StackExchange look the other way. One reason there are no court cases to speak of involving the GPL is IMO because by its very nature there's very little monetary value that can be derived from the software (when you compare to proprietary software) that nobody wants to pay to litigate it. So looking the other way would be easy and the chance of a lawsuit from a 3rd party would be next to nil IMO, although IANAL.
However, and here starts the wildcard: Matt and his inner circle have not embraced WordPress Answers. I initially mentioned the idea on the wp-hackers list and they were, shall we say, less than supportive of the idea (bordering on hostile.) At 47 years old I've been involved in a lot of software communities before WordPress and I've seen the pattern repeat. You have an idealist like Matt who has great instincts and organizational skills and they rise to a significant level of success and generate immense goodwill and lots of fan. However as time moves on they instinctively start to protect "their turf." And my gut tells me that Matt and team view any website that supports WordPress as being "their turf" and thus see it as competitive even if it's actually great for the community of users (as I believe WordPress Answer is.) In this theory anything that might be viewed as competitive with WordPress.org will have a bull's eye on it's back, especially anything that turns out to be wildly successful as I believe WordPress Answers has already proven itself to be.
So there is a potential that Matt may take a stand against WordPress Answers in the same way he took a stand against it his very public campaign against Chris Pearson's Thesis. Matt used the tremendous influence he has generated since founding WordPress to pressure Chris in the court of public opinion and he won. Somehow the community pressure on Chris combined with the threat of an actual lawsuit was enough to get Chris to change his position after saying he never would. So if Matt chooses to view WordPress Answers as the enemy there may be real problems ahead.
BTW, I think Matt did himself some damage by pressuring Chris in the manner that he did. Nothing he can't repair but there are now more than a few people who ask whether Matt really is as benevolent as they used to think. If Matt were to go after WordPress Answers I think his reputation and that of WordPress would take a much larger hit than it did with the Thesis/GPL fiasco.
StackExchange OTOH could just say "to hell with this" and drop WordPress Answers. They don't need WordPress nearly as much as WordPress can benefit from them, at least IMO.
Or StackExchange could choose fight on principle and if so I'm almost positive they would win. To support his opinion that themes and plugins must be GPL Matt references legal opinions on the matter from the Free Software Foundation and the Software Freedom Law Center that supports his position. Of course Matt quoting FSF and SFLC on interpretation of the GPL is similar to Republican US Senators quoting the Heritage Foundation and the Cato Institute as authorities on what should be proper US tax policy; all four of those organizations are advocates for an ideology so their opinions are by definition biased. We can't take the FSF and SFLC's opinion as fact; it will only ever be resolved if the issue were to make it to court (and I have a friend who is a very high profile IP attorney and having discussed the issue with him he believes that in fact a court would not find themes or plugins to be derivative works of WordPress and thus not required to be distributed via GPL if it were ever to be litigated.)
Then there's another angle, and this is probably the most relevant. StackExchange has a rock-star team of investors) and Automattic's has significant investors and I think they would get together and put an end to any nonsensical dispute between StackExchange and WordPress. The investors likely didn't step in when Matt went after Chris Pearson because Chris' company wasn't VC-backed. But Joel and Jeff are different than Chris; have a dream team behind them and are not likely to come off half-cocked in public as Chris did. So I just don't see the WordPress Foundation choosing to battle StackExchange to support Matt's position on the GPL.
Which brings me to the first point I said I'd revisit and that is the issue with CC and GPL not being compatible permeates all the programming sites in the StackExchange network. If this hasn't come up before it probably will and this I'm pretty sure StackExchange will have to address it. And it seems to me that they could do so by simply changing their policy and start dual licensing cc-by-sa for content and GPL for code and require all users to explicitly opt out or have their content removed.
Anyway, I had no idea I was going to write so much. If you made it thus far, thanks for reading.
Hope this helps.