I have some old HTML messages, primarily I think from Eudora, which display as the HTML source code, and not as rendered text.

Some of them are OK, a few others display just the HTML code stream.

Is there any way to force them to render as HTML?

One awkward way is to copy the body of the message (the HTML code) and save as a file, and then create a new message, and then attach file as "insert as text".

Any better solutions? And idea why this happened? (Outlook 2010)

A typical good email has headers that look like this:
Mime-Version: 1.0
Content-Type: multipart/alternative;
boundary="=====================_629154155==.ALT"
Content-Length: 5289


Bad ones like this:
Mime-Version: 1.0