The AttachmentCount extension adds an optional column to the Thunderbird thread pane showing the number of attachments in a message. Features include:
- Shows the count or an icon for a single attachment
- Indicates whether all attachments are detached or deleted
- Tooltip preview for text attachments (and for binary attachments if really desired)
- No need to select a message to get an accurate indicator
See the above link for more details and downloads. Comments welcome.