Typographer extension in the Goldmark Markdown parser, which Hugo uses, has a number of issues with smart quotes. Here are two web pages demonstrating the issues:
Sadly, it seems the author is not a native English speaker and does not feel able to deal with the smart quotes issues, he says “I welcome PR from native English writers.” So far no one has stepped up with a PR, the issue has been marked as stale and closed.
Here was a bug report for Hugo, which was closed because the bug is upstream in Goldmark.
Can anyone figure out a solution and/or submit a PR for Goldmark? Since Blackfriday has been deprecated, there does not seem to be a good workaround.