I have found that the smart-quotes option of org-mode does not export properly the quotes when they are nested (single quotes inside double quotes), but only when they coincide at the start or the end of the quote.
Maybe the problem will be clearer with an example:
#+TITLE: Smart quotes example #+OPTIONS: toc:nil ':t #+LANGUAGE: en #+LATEX_CLASS: book She said to me: "Rick screamed, 'let's go together'"
This gets exported to TeX as:
She said to me: ``Rick screamed, `let's go together'''
Which gets rendered as PDF as:
The order of the closing quotes gets reversed, it first closes the outside double quotes and then the nested single quote.
I have tried leaving a space between them, but that is arguably worse
She said to me: "Rick screamed, 'let's go together' "
She said to me: ``Rick screamed, `let's go together' "
In this case, the internal single quotes are rendered correctly, but the closing quote is not converted into its "smart" version.
If the nested quotes are in such a way that there are other characters between the quotes, that is they are not together at the start or the end of the quote, they get rendered correctly.