Really it is dpown to the browser not liking those quote marks, it looks like they are using the Left double and right Double quotes.
either they should be replaced strait quotes, or they should be converted to HTML Entities, for example:
<p>Alpha meaning “denoting the dominant animal or human in a particular group” (Oxford English Dictionary)</p>
see this page for details:
most keyboards don't have keys for Left and Right curly quotes, so you wont be able to type them. They come from a word processor like Microsoft Word.
if your client is creating the content in MS Word, make sure they are using the Past From Word toolbar option in the CMS toolbar.