Stephen,
It is not clear to me in the case where there is a weird name, how having them in an Attachments folder would aid in finding them? I have always appreciated the fact that Mail kept the attachments with the message text content.
To clarify the purpose of the Mail Downloads or other designated folder, it came about in Mail 2.x in Tiger, and is meant to allow temporary storage when other apps might be used to edit an attachment (such as with a Word doc) and then return the edited file to the original sender or others. In the cases where the attachment gets placed in the Mail Downloads folder, that copy is totally redundant to what is kept with the message, but the one in the message can never be altered. This is why in Mail Preferences/General you see a selection about when to remove any files from the Mail Downloads folder, and most people would choose to have that take place when they next close Mail, or some short time duration.
To Save an attachment, beginning with Mail 3.x and Leopard, the Save button can be used in two ways. If you make a quick click on the Save button in each message, all the attachments get placed into the aforementioned Mail Downloads folder. If you click and briefly hold on the Save button, you can easily get a dialogue to allow you to choose where you want to permanently save any or all attached files, and name the folder, etc.
In Mail 3.x, with IMAP accounts, within the actual mailboxes, there came into use an Attachments folder -- again redundant to the copy kept with the message, but providing a cache location for any attachment actually downloaded, which with IMAP could either be by the setting when downloaded to be kept as a copy for Offline viewing, if not set to do that, upon actually clicking on a message to display and read.
In Mail 4.x & Snow Leopard, the Attachments folder has been added to the xxxx.mbox folders of POP accounts -- again redundant to the copy stored with the message, and the file goes into the Attachments folder at the time of download whether yet read or not. I have not explained the need for this folder with a POP account, and am concerned that the redundancy will balloon storage requirements, and I am trying to find out more about that.
Ernie