Another thing I experienced yesterday.
An admin selected the content of a direct message, quoted it, and copy-pasted the result in our moderation private category. It looked like this (I’m allowing myself to show it since there absolutely no sensitive information):
So I clicked the quote’s title to see the topic (which led to one of the last messages, not the first message of the direct discussion):
I liked both messages because I first thought it was a public topic. The only clue on my screen that indicated it was a direct message where I wasn’t a participant was the user list under the title, in the header… On which my attention was absolutely not focused. Because I was reading the messages.
I scrolled up to read the other messages and the first thing I saw was the envelope icon in front of the topic’s title (I could have seen the section with the participants, but again, my brain ignored it):
So I realized my “mistake” and un-liked the messages.
Obviously, I understand that I was able to see the topic’s content as I was an admin.
But maybe some sort of similar warning (see my first post and other people’s suggestions) could be set-up? Maybe a popup warning when clicking the topic’s link, similar to what @RGJ suggested, something like “you’re about to see a direct message in which you’re not a participant” or something like that?
I’m not sure. I didn’t face this issue for 3 years using Discourse, so it might be a rare case… But anyway, my little mistake happened and it’s very possible that I could have even replied to the topic without even knowing it was a direct message in which I was not included, which could trigger an issue (regular users seeing an admin directly replying in their “private” discussion 
)