Game Of Thrones: 15 Plot Threads The Show Totally Abandoned
2. Jaqen H'ghar
Yes, a man was there to train a girl, but long before Jaqen (or the person with that face, at least) was teaching Arya how to mop floors and clean corpses for hours on end, he was in the Black Cells of the Red Keep, and that's where the real mystery lies.
We still don't know if the first Jaqen, the one who was in the Cells, is the true identity of the person, or simply one of the many faces a man has worn. Whether he really was just a criminal who was assumed by the Faceless Men, or a Faceless Man all along.
On top of that question, we're left with a trained assassin who can change his face either being imprisoned, or taking the place of someone who was, either of which would've been a deliberate act, but without any explanation of WHY they did so. Or what duties he was attending to during Seasons 3 & 4.
As if those Faceless Men mysteries weren't enough, there's then the fact that Arya has some faces with her when she arrives at Winterfell, and yet never uses the training again (that we see, anyway).