What's going on with the phrase: "none the wiser"?

Yes, it appears to be an archaic usage of none:

Middle English non, none, from Old English nan "not one, not any, no person; not the least part," from ne "not"...

since c. 1600 reduced to no except in a few archaic phrases, especially before vowels, such as none other, none the worse.

(Etymonline)

The earlist instance of "none the wiser" that an Early English Books Online search finds is from Ben Jonson, Volpone, or The Foxe (1607), act 4:

Politiqve. My first is / Concerning Tinder-boxes. You must know, / No family is, here, without it's boxe; / Now Sir, it being so portable a thing, / Put case, that you, or I were ill affected / Vnto the State: Sir, with it, in our pockets, / Might not I go into the Arsenale? / Or you? come out againe? and none the wiser?

Here the sense of "none the wiser" seems to be "no one would be any the wiser"—that is, no one would be aware that the speaker—or the person being spoken to—had slipped into the Arsenal with a tinder-box in his pocket that he could have used to blow the place up.

And likewise, from Nathan Field, Amends for ladies: With the Humour of Roring (1618):

Ingen. Shall we then / Couple vnlawfully? for indeed this marrying / Is but proclaming what we meane to doe; / Which may be done priuatly, in ciuill sort / And none the wiser, and by this white hand La: / The wrack, Strapado, or the boiling boote, / Should neuer force me tell to wrong your honor.

But an instance of "none the wyser" appears in a 1537 translation of The History of Kyng Boccus, [and] Sydracke How He Confoundyd His Lerned Men, and in ye Syght of Them Dronke Stronge Venym in the Name of the Trinite [and] Dyd Hym No Hurt (1537?):

For euery erthely man wyl nought / Tel to euery man his thought / Ne his wyl in preuyte / But yf he preuy with hym be / Also reserueth god hym to / Many thynges that he wyl do / That he wyl of no kowlegynge / Geue to man / ne to nothynge / But to his owne sone onely / For he is next and most hym by / And that tyme that goddes sone / Shal in erthe a man here wone / Men shal hym aske yf the worlde here / Shal endure seuen thousand yere / And anone answere he shall / And saye ye / and more withall / For of the fathers preuyte / Of the more / shal none the wyser be

Earlier still is the first instance EEBO finds of "never the wiser." From Ranulf Higden, Prolicionycion (printed by William Caxton sometime after July 2, 1482):

Speche is not knowen but yf it be lerned comyn lernyng of speche is by hering· & so alway he that is deef is alway dombe for he may not here speche for to / lerne / So men of fer countrees and londes that haue dyuerse speches / yef neyther of hem haue lerned others langage / nether of hem wote what other meneth / though they mete and haue gret nede of informacion and of loor of talkyng and of speche be the nede neuer so grete neyther of hem vnderstondeth others speche no more than / gaglinge of gees For Iangle that one neuer so fast that other is neuer the wyser though he shrewe hym in stede of good morow·

...

Thenne the forsayde lewde reason is worthy to be powdred· leyed a water and y soused Also holy wrytte in latyn is boothe good and fayr / And yet for to make a sermone of holy wrytte al in latyn to men that can Englysshe and no latyn / it were a lewd dede / for they be neuer the wyser / For the latyn but it be told hem in Englysshe what it is to mene

The construction "never the wiser" means something like "at no subsequent time and in no respect any wiser." Higden died in 1364, so the phrase "never the wiser" is indeed quite old.