Eudora (New Version Based on Thunderbird)
For the new Eudora, which is based on Mozilla Thunderbird, you need select the message in question and go to "View > Message Source" to access the message source.
Eudora (Original Version)
For the older versions of Eudora, you need to double click on a message to open it in a new window. Then click on the "blah blah blah" icon at the top. This will show you all of the headers for the message.