How can I tell what dungeon paths...
Last time I checked, it wasn’t possible. The only advice I can give you is “check if you can launch the dungeon in explorable mode”. That will tell you if you did Scenario mode or if it counts in the paths you didn’t yet complete.
You can do that easily when you use MS Excel® (or similar) and write down each path of each you ran.
Checking for story mode is possible – as Sacrai described.
Yeah, I don’t run enough dungeons to do a spreadsheet. I think I have maybe run 6 times total since the game came out. I was just curious.
sadly there is no way, but it may help to remember key points and ask those that have done them all. compare notes on bosses or key points of interest (the one with the jellyfish, the one with the burrows, the one with the giant hammer ooze of pain, etc..)
the only way I keep up with it is by picking a day with my guild and running all the paths in that one dungeon in one day. keep it fresh and its harder to lose track.