There are actually several feature requests in JIRA's JIRA (is that like inception?) to support attachment obsolescing. However, I did find this helpful tidbit on a mailing list:
Trick: upload the file with exactly the same name, then the latest one will be marked as "latest" (in mouse-over baloon), and earlier versions will be shown in gray.
And this helpful tidbit on a JIRA, directly from a JIRA developer:
At the moment JIRA does allow one to attach files with the same name to the issue and JIRA greys out the older files with the same name, such that visually one can tell which attachment is the newest. Does this work for you?