Drupal 7.39 CiviCRM (in this case 4.6.7)
We can't find any way to search for activities with attachments.
Am I missing something obvious?
Similar to this question: Search contacts with attachments
This might be an answer to a slightly different question, but... in the past, I've used a mix of add-ons to perform a full-text search on activities and their attachments:
When you run a search with "Search => Full Text" and filter on activities, it will include any matches in PDFs/DOCs/etc that are attached to activities.
That module may be a significant undertaking (e.g. it requires an extra server, Solr, and the documentation is pretty rudimentary), but if you really need it, it might be a piece in the puzzle.
I've customized the Activity Report to display which activities have attachments. I don't think I added a filter to show ONLY records with attachments, but that's just another line or two of code. I've uploaded a copy to github here: https://github.com/PalanteJon/activityAttachmentReport/tree/master
Note that these aren't the only customizations I've made in this report, but you can search for "attachments" in my code to see how I added attachments to the report.