As discussed under this comment thread, we would not be able to include works under fair use in our posts. This is because (from the current TOS):
You agree that all Subscriber Content that You contribute to the Network is perpetually and irrevocably licensed to Stack Exchange under the Creative Commons Attribution Share Alike license. ... Subscriber warrants, represents and agrees Subscriber has the right to grant Stack Exchange and the Network the rights set forth above.
Where "Creative Commons Attribution Share Alike license" will be interchanged with a new license at some point, but the problem remains. The problem is fair use only allows you to use a work. It never allows you to license the work to someone else, especially for all the licenses we are considering. You also can't decide not to follow the TOS by putting a note saying "This was taken from fair use. Don't use under license", because you are still violating the TOS; you're just admitting it.
Therefore, I propose we put something along the lines of "... except you don't have to give us the license to stuff you are using under fair use from other people."
SE has to update their TOS anyway when they change licenses, and this will allow us to continue to import content from Wikipedia, even after we migrate away from creative commons.
NOTE: Wikipedia has done this already with for when their contributors want to use something under fair use. See Exemption Doctrine Policy.
NOTE: This appears to be patched in CC-BY-SA v4 (although it would require more discussion), since it explicitly puts
2.a.2 Exceptions and Limitations. For the avoidance of doubt, where Exceptions and Limitations apply to Your use, this Public License does not apply, and You do not need to comply with its terms and conditions.
So you can license the work to SE without giving them unlimited use of the fair use works. So maybe also updating the text to CC-BY-SA v4 would be in order when we change the code license.