I believe tomizza has made the best summary, but I think I can add one more piece to the puzzle:
I do indeed view my messages in Plain Text by default — and I like it that way. The problem seems to be when the attachment is embedded in the Rich Text (HTML) version of the message. Mail, being the good citizen that it is, sends out both a plain text and rich text version of your message if you create it in rich text. Unfortunately, the current version of Mail does not parse the HTML version for embedded attachments, which is where the problem attachments seem to be located. Here's an example (raw source, edited):
*****************************************
--Apple-Mail-319-850405842
Content-Type: text/plain;
charset=US-ASCII;
format=flowed
Content-Transfer-Encoding: 7bit
Am I on the right track?
--Apple-Mail-319-850405842
Content-Type: multipart/mixed;
boundary=Apple-Mail-320-850405842
--Apple-Mail-320-850405842
Content-Type: text/html;
charset=US-ASCII
Content-Transfer-Encoding: 7bit
<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">
Am I on the right track?
</body></html>
--Apple-Mail-320-850405842
Content-Disposition: inline;
filename="F06 Stats.pdf"
Content-Type: application/pdf;
x-mac-type=50444620;
name="F06 Stats.pdf";
x-mac-creator=4341524F;
x-unix-mode=0644
Content-Transfer-Encoding: base64
JVBERi0xLjQNJeLjz9MNCjU1IDAgb2JqDTw8L0xpbmVhcml6ZWQgMS9MIDI4Mjc5NS9PIDU3L0Ug
MjY1MzMzL04gMS9UIDI4MTY1My9IIFsgNjU2IDE4Ml0+Pg1lbmRvYmoNICAgICAgICAgICAgICAg
[...]
--Apple-Mail-320-850405842
Content-Type: text/html;
charset=US-ASCII
Content-Transfer-Encoding: 7bit
<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">
</body></html>
--Apple-Mail-320-850405842--
--Apple-Mail-319-850405842--
*********************************************
As a sender of messages, the best workaround (and the best policy, IMO) in Mail is to send your messages in plain text mode. As a reader, you can use the previously mentioned techniques.
I don't believe the problem exists in Tiger, so I think this is a Mail bug.