You may find that with a Joomla 3 installation, suddenly there are slashes in front of every apostrophe in your content. It can be a little maddening.

What is happening is that somehow a Magic Quotes setting is set to ON in your site's PHP settings. This is controlled by your hosting company and they may or may not be cooperative helping your with this particular problem.

Override your sites PHP settings

You can try putting a little php.ini file in your root directory that is supposed to turn of magic quotes. Open a text editor like Notepad++ and create a new document.  Add these lines: 

magic_quotes_gpc = Off
session.save_path = "/tmp"

Save this document as php.ini. Upload this file to the root of your website's file system.

Try making a new article, put in some apostrophes and save.  If the apostrophes do not have slashes placed in front, then you are good to go.

Hack the core

If this doesn't work, try the following hack of the core files (I don't recommend hacking core files - but sometimes it comes to this).

Using and FTP prograpme or your host's file manager, navigate to this file:

administrator/includes/defines.php

Make a copy of this file and rename it 

administrator/includes/defines-orig.php

Download the original version for editing. Add these lines to the bottom of the page:

//Emulate magic_quotes_gpc off
if (get_magic_quotes_gpc()) {
$process = array(&$_GET, &$_POST, &$_COOKIE, &$_REQUEST);
while (list($key, $val) = each($process)) {
foreach ($val as $k => $v) {
unset($process[$key][$k]);
if (is_array($v)) {
$process[$key][stripslashes($k)] = $v;
$process[] = &$process[$key][stripslashes($k)];
} else {
$process[$key][stripslashes($k)] = stripslashes($v);
}
}
}
unset($process);
}

Save this file back to the name defines.php. Upload this file back to the same directory.

Test out this method with a new article containing apostrophes.

Hopefully one of these mothods will help you out. Remeber that this defines.php file will be overwritten if you upgrade Joomla.