Why didn't The Doctor or Clara recognize Missy right away?

So after it was established that Missy is actually both

the Master, and the "woman in the shop" who gave Clara the TARDIS number...

...why didn't The Doctor or Clara recognize her right away? I remember the Tenth Doctor in The Sound of Drums stating that Timelords had a way of recognizing other Timelords no matter if they had regenerated. And Clara should have recognized her as well...

I'm hoping for a better explanation than "Moffat screwed up", and that I actually missed something after two watchthroughs of the episode.

Answer

There seems to be a lot of in-canon uncertainty as to the extent to which Time Lords can recognise one another which far pre-dates Moffat's tenure. From the Time Lords page on Wikipedia:

Whether or not Time Lords can recognise each other across regenerations is not made entirely clear:

• In The War Games, the War Chief recognises the Second Doctor despite his regeneration and it is implied that the Doctor knows him when they first meet.



• In The Three Doctors the Second Doctor recognises the Third Doctor immediately, despite the fact that the Third Doctor is, obviously, a future incarnation of himself.


• In Planet of the Spiders, the Third Doctor has trouble recognising his former mentor.


• In The Deadly Assassin,[19] Announcer Runcible, an old classmate, recognises the Fourth Doctor despite his changes in appearance and mentions that the Doctor appears to have had a "face lift" since they last met.


• In The Armageddon Factor,[36] Drax, another alumnus immediately recognises the Fourth Doctor, though the Doctor does not recognise him.


• In The Five Doctors,[37] the Third Doctor is unable to initially recognise the Master in his non-Gallifreyan body.


• In The Twin Dilemma,[38] the Doctor's old friend Azmael fails to recognise him, as the Doctor has regenerated twice since their last encounter.


• In Survival, The Master recognises the Seventh Doctor on sight,[39] although this may simply point to an earlier, unseen encounter.


• In Doctor Who (1996), the Eighth Doctor is unable to recognise the Master while he possesses a human body.[40]


• In "Utopia", the Tenth Doctor does not recognise the human form of the Master, although the Doctor did recognise him, and name him "Master", as soon as he recovered his Time Lord physiology and mind.


• In "The Sound of Drums", the Doctor states that Time Lords can "always" recognise each other, although, while on Earth, the Master used satellites with a telepathic network to mask his presence from the Doctor. The Doctor in this circumstance appears to only be referring to recognition of the individual as a Time Lord, not necessarily the specific identity. However when he sees the Master on Television he recognizes him.[29]



• In "Time Crash", the Fifth Doctor could not instinctively recognise that the Tenth Doctor was a Time Lord, much less one of his own later incarnations (this is in stark contrast to the aforementioned "The Three Doctors".)


• In "The Next Doctor", the Doctor initially seems unable to detect that the human Jackson Lake, who identifies himself as the Doctor, is not actually his regenerated future self.


• In The End of Time, the Doctor immediately recognises an unidentified elderly female Time Lord on sight, and also refers to the lead Time Lord by the name Rassilon (an earlier incarnation of Rassilon had appeared in "The Five Doctors"). In the context of the story, however, he may have encountered both during the Time War, though he himself has regenerated since they last saw him. Rassilon and the Woman recognized the Doctor on sight as well, but the Doctor's presence, regardless of incarnation, was expected.


• In "The Day of the Doctor", the Eleventh Doctor quickly recognises the Tenth Doctor, and, later, both of them immediately recognise the War Doctor, although he doesn't realise that both Doctors are his future (asking them whether they're "his companions"). Later in that episode, the Time Lords recognise all the past incarnations of the Doctor, as well as a future incarnation, though this may be due to The Doctor's TARDIS being stuck in the form of a Public Call Box."

I'd suggest whether Time Lords can recognise each other is subtly different to whether they always will recognise each other. In the same way as humans can easily recognise one another, yet you can still walk by a long time acquaintance in the street and not realise it's them (yet if you'd concentrated on them you'd have realised instantly).

The above also mentions a couple of other possibilities - either Missy was using some kind of cloaking technology to hide her true identity, or she's not there as part of a standard regeneration and is somehow using a human host body.

Clara's explanation is a little simpler. She's human, she spoke to this woman briefly in a shop over a year ago (assuming she even spoke to her in person). I probably couldn't pick the woman who served me at the supermarket a week ago out of a line-up, even though she was friendly enough. Even a little disguising would have rendered Missy completely unmemorable.