This page describes Thunderbird's configuration options for attachments.
Specify where attachments are saved
Configure what happens when I click on attachments
Allow me to view "hidden" attachments
There is a special view mode for messages which allows you to see all of a message's attachments, even "hidden" ones, in its attachments list.
Because this view mode is not needed by most users and could be confusing to some, it is disabled by default. To enable it, install the "Show All Body Parts" add-on.