Essentially, it's the remark that Jaqen H'Ghar's second face is strangely similar to the face of Daario Naharis (the resemblance to the Alchemist in Oldtown is well known, no need to insist on this).
First the evidence. Here is Jaqen when he changes his face (Arya, ACoK).
He grinned, revealing a shiny gold tooth.
Here is the Alchemist (Prologue, AFfC)
All elements are there, except the most significant one, the golden tooth. The description of Daario is scattered throughout various chapters. GRRM is careful not to ring our alarm bells by changing the vocabulary and making Daario dress flamboyantly. Here are the relevant passages (all from Daenery, ASoS, except the last one from ADwD)
Daario was fair where Jorah was swarthy; lithe where the knight was brawny; graced with flowing locks where the other was balding, yet smooth-skinned where Jorah was hairy. And her knight dressed plainly while this other made a peacock look drab, though he had thrown a heavy black cloak over his bright yellow finery for this visit.
His hands were large and strong, and there was something in his hard blue eyes and great curving nose that suggested the fierceness of some splendid bird of prey.
A golden tooth gleamed in his mouth when he smiled.
tracing his scars and making him tell her how he’d come by every one.
The elements are there (golden tooth, hooked nose, curly hair) except perhaps the facial scar. The scar is easily visible on Jaqen. The presumed identical scar is barely visible on the Alchemist, who has a shadow of a beard. Therefore such a scar would likely be hidden by a full beard, like Daario's. Dany notes scars when in bed with Daario. We can suppose that Dany could see or touch the scar behind the beard when she is close to her lover. But it's not said explicitly that there is a facial scar.
It's unlikely to be a coincidence for two reasons:
1) The first reason has to do with numbers. There are three golden teeth mentioned in the whole series (Jaqen, Daario and Garin the orphan, if we discount Mord the goaler whose tooth only appears in the show, as Frey Pie remarked in the original thread). I counted ten hooked noses in the books (Jaqen, Daario, the Alchemist, four Kettlebacks, Sandor, Hos Blackwood, Asha). Curly hair are not very common (the Lannisters' curly hair are often mentioned though).
2) Jaqen's second face has several specific and uncommon features, so that we could recognize the face. It's unlikely that GRRM reproduced them deliberately in the Alchemist and by accident in Daario.
If one accepts that it is not a coincidence, it means that Daario could be a Faceless Man. I see mainly two lines of explanations:
a] Jaqen, the Alchemist and Daario are the same person (the same... no one so to speak).
b] The same face has been dispatched to several agents by the Faceless Men.
I can't say much about b]. I would be pleased to see arguments for or against a].
The option a] implies that Jaqen went to Meereen as Daario, then came to Oldtown as the Alchemist and went back later to Meereen as Daario. I admit it is convoluted, but it is not precluded by the timeline. Briefly, here is why.
There was enough time to disappear from Harrenhal and reappear in Meereen between the middle of ACoK and the middle of ASoS. During the first part of ADwD, Daario is sent to a long mission to Lhazar and Dany knows nothing of his whereabouts. We don't know when Daario left Meereen for the mission. When the Alchemist is in Oldtown, Tywin Lannister is still believed to be alive. Tyrion left King's Landing after the death of Tywin (obviously) and reached Meereen almost three monthes after Daario (who arrived in Meereen ninety days before Dany's marriage), and his trip was suboptimal because of the long journey along the Rhoyne and various misadventures.
There are a few details in favor of option a]:
– The Alchemist arrives in Oldtown precisely when rumours of dragons in Meereen reach the city. That might not be coincidental. Indeed, the Alchemist could have been in the same ship that brought the rumours.
– If the Alchemist is in search of the fabled book on dragons hidden in the Citadel, it makes good sense that he is (or is an agent of) someone well aware of Dany's situation with the dragons. Who in Westeros could qualify?
And a few problems:
– Daario's behaviour and personnality might seem at odds with being a Faceless Man.
– How could Daario have left the Stormcrows to accomplish the mission in Lhazar?
More observations and details are to be found in the original thread. (For the record, I shall say that I am not particularly fond of the idea that Jaqen is Daario.)