Sorry this didn't get replied to sooner.

The condition failed is defined in exim's default config file
40_exim4-config_check_data

quoting from the exim spec (aka manual):
BEGIN_QUOTE
This condition is relevant only in an ACL that is run after a message has
    been received, that is, in an ACL specified by acl_smtp_data or
    acl_not_smtp. It checks the syntax of all header lines that can contain
    lists of addresses (Sender:, From:, Reply-To:, To:, Cc:, and Bcc:),
    returning true if there are no problems. Unqualified addresses (local parts
    without domains) are permitted only in locally generated messages and from
    hosts that match sender_unqualified_hosts or recipient_unqualified_hosts,
    as appropriate.
END_QUOTE

After reading that, I quickly see the problem: -email is unavailable- <bug-gnulib@gnu.org>
The first @ in that address is not valid.

Hi,

When submitting some test results, I got the following delivery fail report:

<bug-gnulib@gnu.org>: host eggs.gnu.org[2001:470:142:3::10] said: 550 Message
    headers fail syntax check (in reply to end of DATA command)
<coreutils@gnu.org>: host eggs.gnu.org[2001:470:142:3::10] said: 550 Message
    headers fail syntax check (in reply to end of DATA command)

The email in question seems valid, and after removing colons from the body of the email, a delivery succeeded.

I've attached the e-mail I originally attempted to deliver.

This email is parsed correctly by both Postfix and Emacs.

We've attempted delivery from two different mail servers, and both failed.