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My guess is the author is not creating/editing the post in their browser. Rather, they are using a desktop application, like M$ Word, which uses non-standard character entities, especially for 'curly quotes', and then pasting the text into their post. Or, they may even be using an email client that does the same thing.
It has nothing to do with your host or site. Find out how the author is editing and adding posts and you will discover the source. As for cleaning it up, you will have to edit the posts and correct the characters.
Edit: I see what you mean about changing the character encoding. You might change the character set by editing your theme :
<meta http-equiv="content-type" content="text/html; charset=ISO-8859-1" />