Hello. I'm the author of the Contact Form 7 plugin. I found some problematic codes in Jetpack's newly introduced contact form module which block other plugins from working.
The problem is in the contact_form_widget_atts() function which is used as a filter for widget_text hook. Especially this line:
return str_replace( '[contact-form', '[contact-form widget="' . $widget . '"', $text );
Contact Form 7 allows to use its shortcode like
[contact-form-7 id="1234"] in text widgets, but Jetpack's above function replaces it to
[contact-form widget="1"-7 id="1234"] and it behaves as Jetpack's shortcode.
I hope Jetpack developers take care of this issue and fix it in the future release.