Yes, i noticed last night, the objective clears as soon as you enter, and "you are good to go", but when you turn in with Mordra she thinks you cleared the place..
Here, look:
And thats exactly what the objective SHOULD be, right? Or am I Undanted for just opening a door and leaving?
So yea, you might be right tho, its not actually a bug. But it does sounds like it's wrong man.
Whats worst is.. I went there alone and sat outside the door for 10 to 15 minutes waiting for players to gather up with me and go for it, and for 10 to 15 minutes I saw people coming and leaving, some went in and out in a blink, and i saw a range of lvls like 8 to 16, and about 10-12 different players.. Until this guy lvl15 stops in front of me and talks to me. We gruoped up and cleared it.
So it seems to me that a lot of people get the undanted initiation for "free". Dont call it a bug, but its clearly wrong to me. If I could, i'd make so objective clears after opening the EXIT door, or killing the last boss - like the fighters guild, i noticed i got xp for fighters guild when i killed the boss..
The Undaunted intro quest is a joke. Just some colorful dialog of Undaunted people thumping their chests. You are told to visit the dungeon, and simply entering the door satisfies the quest, and you're done. It's working as designed. It's just that the design is rather poor. Nothing that teaches people about dungeons in general, about the "trinity" of roles in group PvE, etc.
Compare this to the intro quests for Cyrodiil and for crafting, and you'll see what I mean when I say that this question is useless.
[A solo quest to teach dungeon basics] is a great idea. I think this would be most easily incorporated by making it part of the Undaunted recruitment quest "One of the Undaunted". Change the requirements of that quest so that instead of just having to set foot inside the first zone's Group Dungeon by yourself (you don't even have to clear the dungeon to complete the quest), you are sent to an instanced dungeon with 3 NPCs.
Logically, these NPCs would be Turuk Redclaws, Mighty Mordra, and Kailstig the Axe, as they are the three recruiters. This would be a short instance introducing the group dungeon mechanics and would have you take on the role of tank, healer, ranged DPS and melee DPS in sequence. If you don't have the appropriate weapon/class skills, you would be temporarily given access to a resto staff and Grand Healing for the healer section, a mace/shield and Puncture for the tank section, a bow and Poison Arrow and/or a destro staff and Destructive Touch for the ranged DPS section (your choice of either or both), and a battle axe and Cleave and/or dual daggers and Twin Slashes for the melee DPS section (your choice of either or both). The three recruiters would take on the roles that you are currently not exploring so that the setup is always 1 tank, 1 healer, 2 DPS.
In line with the suggestion above, successful completion of this short tutorial quest would be required to unlock the Dungeon Finder. Additional characters on the same account would not need to complete the quest again, but could if they wanted to.