I am using version 3.8.4 of the plugin now.
I have a Newsletter dedicated page which is set up from “Subscription Steps” -> “Newsletter dedicated page”.
It has in its body the [newsletter_form] shortcode.
I found the problem – it is the newsletter\subscription\subscription.php file the function shortcode_subscription – the form tag isn’t closed before returning the buffer.
And also I misconfigured the plugin by setting the page with the [newsletter_form] shortcode as a newsletter dedicated page.
I just didn’t notice that a newsletter dedicated page should contain the [newsletter] shortcode.
Yes, we’re fixing it and we’re reviewing the short codes to more coherent and easy to use. The [newsletter_subscription] short code is still experimental and yes, there are few errors with it which I’m fixing.