On my map selection screen, my Hobbler's Hold and Random Run dungeons have a gray background with a red exclamation point. The rest are black.
The dungeons do not seem to be different in any way, and going on the run doesn't clear the marker. Way back in the day, I recall a similar marker existing for dungeons where I could still unlock an item or quest or something, but it doesn't seem to do anything now. Is this possibly a bug?