If your font is, for example, Georgia Italic, Smashwords won't recognize that the text is meant to be in italics. Eventually, you may realize that Smashwords wants you to use Georgia Regular, with italics applied.
Yes, this so make a person's head hurt.
I managed to change the font using NeoOffice, an OpenOffice clone for the Mac. Basically, I searched for "Georgia Italic" and replaced it with "Georgia, Italic."
I dunno if posting this will help anyone, but it might help me the next time I run into this problem.
Dear Smashwords, please start accepting epub files soon!