Thunderbird won't display images containing in collected email

It's not possible to say without seeing the raw source of the message in question, but my best guess is that the message contains incorrectly formatted HTML code. This would be the fault of the sender, not of Thunderbird or Windows.

The problem is with ALL the messages, not just this one. I should have made this a little clearer when I first asked the question. This was the only message that solicited the response that I quoted.

The default setting in Thunderbird is to NOT show external images... for very important reason that it's a security risk. You can override this behavior with the settings found at <Settings | Privacy & Security | Privacy | "Allow remote content in messages">. But if the images are not directly served at the indicated link, or that link is redirected elsewhere or by a script, Thunderbird will not display them.

I think the one message that shows the "message requires formatting features that your email client does not support" is a separate issue, unrelated to the image thing. It probably is actually due to messed up HTML, or perhaps because of the presence of a TNEF attachment, which is an antiquated, proprietary attachment format generated by some Microsoft products. We don't see it much anymore, but they may still be floating around somewhere.