If your WordPress database is filled with weird characters (For example, if you pasted something from Microsoft Word…) the following recipe will solve the problem by replacing those characters by the correct characters.

Simply run the following SQL query on your WordPress database, using the command line client or PhpMyAdmin. This will remove weird characters from all your posts and comments.
Don’t forget to backup your database before using this query.

 UPDATE wp_posts SET post_content = REPLACE(post_content, '“', '“'); UPDATE wp_posts SET post_content = REPLACE(post_content, '”', '”'); UPDATE wp_posts SET post_content = REPLACE(post_content, '’', '’'); UPDATE wp_posts SET post_content = REPLACE(post_content, '‘', '‘'); UPDATE wp_posts SET post_content = REPLACE(post_content, '—', '–'); UPDATE wp_posts SET post_content = REPLACE(post_content, '–', '—'); UPDATE wp_posts SET post_content = REPLACE(post_content, '•', '-'); UPDATE wp_posts SET post_content = REPLACE(post_content, '…', '…');  UPDATE wp_comments SET comment_content = REPLACE(comment_content, '“', '“'); UPDATE wp_comments SET comment_content = REPLACE(comment_content, '”', '”'); UPDATE wp_comments SET comment_content = REPLACE(comment_content, '’', '’'); UPDATE wp_comments SET comment_content = REPLACE(comment_content, '‘', '‘'); UPDATE wp_comments SET comment_content = REPLACE(comment_content, '—', '–'); UPDATE wp_comments SET comment_content = REPLACE(comment_content, '–', '—'); UPDATE wp_comments SET comment_content = REPLACE(comment_content, '•', '-'); UPDATE wp_comments SET comment_content = REPLACE(comment_content, '…', '…'); 

If you like to know more about WordPress SQL queries, you should have a look to this article.

Thanks to Jeff Starr for the cool tip!