Revisiting kingtw's instructions from Apple Support, I tried the following:
1. Moved a message that appeared to be missing its attachments from an On My Mac mailbox to Inbox using Message > Move to > [my Apple ID inbox]. No attachments showed up.
2. With the Inbox selected, chose Mailbox > Rebuild. Mail indicated it was downloading 45 messages (?). In the test email, attachments (photos) now appeared inline as expected and as seen in Mail viewed in iCloud with Safari.
3. Moved the message back to its proper On My Mac mailbox. Attachments seemed to disappear.
I repeated steps 1 and 2. This time the message showed jpeg icons instead of showing the attachments. Quicklook, Save to Desktop and Export to Aperture did not work for the attachments in this message. Without moving the message, I switched to another app and returned to Mail. The jpeg icons seemed to disappear.