Problem Summary: When I try to write a post in my blog all single quotes are replaced with double quotes. Just an example if I write You’ll check it becomes You”ll.
1) Please deactivate all the plugins. Enable plugin one by one and check the result with your post output. Because there is a high possiblity that It may cause the issue with your post/database.
2) Check that magic_quotes_runtime variable setting in the php.ini is turned off on your web server. If it is enable then affects runtime generated data such as data from SQL queries. If it is enable then we can disable it from .htaccess file. Please use this code:
# BEGIN WordPress
php_value magic_quotes_gpc 0
php_flag magic_quotes_runtime 0
# END WordPress