Are there still any unsolved quests?

Did you try saying What Ward?

The Island of Misfit Quests?

Funny, I looked into this for the first time about a week ago, and started searching on the web. If you're using zam as a "all completed quests " guide, reading some forums posts form different sites, I think there's probably thousands.
I started in Qeynos, reading a lot of posts and talking to NPC's, the story lines are pretty complicated. A lot of quests (possibly new expansions to?) you need to use combinations of words that aren't even the dialogue the quest giver speak, and possibly it takes simply knowing the storylines of other npcs.

Example: The glowing black stone is a quest item that has never been solved apparently, I tried to look into it but the story behind it has something to do with the necromancers of Qeynos Hills and the corruption of Qeynos, there's two? "Plaguebringer" members in the hills, though their faction is Sabertooth, so in alliance with blackburrow gnolls (possibly).

The glowing black stone is a rare drop, and if you speak to the plaguebringers, or are able to, they talk about a hierarchy of masters, so it gets very complicated.

And that's the oldest content, where it could take someone 20 years to figure out a quest.

Regarding Glowing Black Stone.

From that same post (yes I'm the same guy that did the big starter post in Ogrish). I noted that Allakhazam had at the time about 8000 quests in its system, 6 years after the video that threw out the 15,000 number. Chances are their metric for a "quest" as used in that video may be simply every instance where an NPC responds to either an item turn-in or a text prompt (and given this is in 2009, I could almost see that including the standard greeting on a Hail).

Personally I think it'd be fun if DPG could consider outsourcing some quest design for the unused items to select players. In the post I made I made a lore case for a Shadow Knight version of Soulfire based on the existing quest text that pretty much all spawned from a case of boredom at being max level in classic with not much else to do.