Ok, you're VERY, very close. The killer are the lousy single and double quotes, which have to be modified ever so slightly.
UPDATE post SET pagetext = REPLACE(pagetext, '"', '"')
UPDATE post SET pagetext = REPLACE(pagetext, "'", "'")
should do it if your original table name and fields (post,pagetext) represent the actual db you're using. (Cut and paste the commands into notepad or whatever so you can read them better if needed- the browser formatting/default text is evil
To make it fly, what I had to do was enclose the single quote-containing text by double quotes, and vice-versa.
I built a quick test data table on my development server and ran it across a couple dozen records with success from the mysql command line.