Usually there is a link below the text to open or save the attachment. But for some emails this link is missing even though the symbol in the list shows that this mail has an attachment.

It does not work for all mails which were sent from "Apple Mail", but I don't know whether this is the only email client with this problem. 
I looked into the source and compared it to other mails and what I found suspicious is the "Content-Disposition: inline;" in those mails from "Apple Mail" instead of "Content-Disposition: attachment;" in mails from other clients.