The solution at that page is fine. The reason it’s generating unexpected output is because you might have accidentally grabbed trailing whitespace when pasting it. If you use this instead:
<?php
/*
Plugin Name: TurnOffSmartQuotes
Plugin URI:
Description: Stops WordPress from converting your quote symbols into smartquotes. The three lines below stop the smartquote conversion in 1) your post content, 2) your comments, and 3) your post excerpts.
Version: 0.1
Author: Katja Stokley
Author URI:
*/
remove_filter('the_content', 'wptexturize');
remove_filter('comment_text', 'wptexturize');
remove_filter('the_excerpt', 'wptexturize');
that should do the trick.
I’m not sure why WordPress isn’t correctly texturizing “didn’t”, but that will fix the problem.