Update: the bug is fixed in WP 3.4.1, you can upgrade now.
There is issue in PHPMailer 5.2.1 bundled with WordPress 3.4: you can not send emails with wp_mail() if php safe mode on.
I found that testing my plugin EasyMail after a lot of reports by users that have problems after upgrade to 3.4. The newsletters and the test email cannot go out: the report always says “failed”…
I found this bug report in trac: http://core.trac.wordpress.org/ticket/20970
You have to manually patch the phpmailer class file, here you are the direct link to the how-to-fix the issue (2 lines of code): http://core.trac.wordpress.org/attachment/ticket/20970/20970.patch