I think these problems
are both minor; in fact I think the second one is only a potention problem but not currently affecting your list. The first is minor in that it used to cause a larger jump in spam scoring that it appears to do now, and the second because your list is so low volume and subscribers can't post to the list.
1. No "Message-Id" email header. The internet email RFCs specify that email must have a Message-Id header, and define what it is and how to make it unique, etc. Many "email transport" programs will add one to any email they receive that is missing this field, prior to passing it on. When I get list posts, the message-id is always added by my local system's email transport software, which means whatever software you use to render and send the emails isn't generating one and the smtp server of your hosting company isn't adding it either. I find it interesting that the email seems to go thru both exim and qmail on your hosting company's servers without a message-id being added, but it is really the responsibility of the program that generates the email to provide this header field.
Spam frequently is generated by programs that don't bother with the message-id. A missing message-id (or one added by the receiving system to an email that originated off-system) is used by some anti-spam detection systems; it will typically not be sufficient to block the email but may raise the 'score' that makes it more likely to be marked/filtered as spam.
Having said that, the spam filtering I use seems to no longer raise the score based on this trait; it used to.
2. No email address verification. I don't think this has you on any blocklists at this time, but that could happen and then it is difficult to get off. Here are some URLs describing closed loop address verification and why you should use it:
If you implement verification there is at least one trap to avoid; if you just send a verification email every time an email is submitted you create a way for a bot to mail-bomb someone thru your website, and that
would be worse than getting subscribed to a one-per-week unverified list, and more likely to get you blacklisted than you are now. You'd be wise to have a daily threshold per email address, but something larger than one.