I worked it out, its the input type of "date". This isn't supported in IE, FF or safari yet.
You need to first edit lines 55 - 62 in contact-form-7>includes>modules>date.php.
Instead of saying:
if ( wpcf7_support_html5() ) {
$atts['type'] = $tag->basetype;
} else {
$atts['type'] = 'text';
}
Comment everything out except the 4th line so it looks like :
//if ( wpcf7_support_html5() ) {
//$atts['type'] = $tag->basetype;
//} else {
$atts['type'] = 'text';
//}
Then install Contact Form 7 Datepicker