I use Word 2002, but 2003 probably works the same way. Sometimes
Smart Quotes has gotten flaky, this has worked -
In the AutoCorrect dialog box,
"AutoFormat As You Type" tab,
"Replace as you type",
check the box: "Straight quotes" with "smart quotes"
Sometimes I have to toggle the box a time or two. Sometimes
restarting Word with a blank document and toggling the box fixes it.
Sometimes then reloading the original file where the problem first
cropped up will then work ok.
If necessary, with the "smart quotes" box checked, do a search and
replace with the dumb quote as both the 'find' and the 'replace' text.
Word will fix the smart quotes as the search and replace operation is
run.
---------------
Just checked the link in Lanux128's post, and I forgot there's also
the same "Straight quotes" with "smart quotes" checkbox in the
"AutoFormat" tab. I haven't had the problem since I changed
machines, but unchecking/checking both boxes always worked.