Ah, Word! You and your quote smart unquote quotes!
Finally got smart and added in a new AutoCorrect rule in Microsoft Office 2010: replace —“ (which is what it loved to do to me, all the time) with —” (which will save me a lot of backspacing. In case you have this problem:
File>Proofing>Autocorrect Options (it’s a button near the top).
To make sure you’re getting left double quotes and right double quotes, use the Character Map to insert those marks in the appropriate fields.