I'm no expert on memory, but Q makes what seems, to me at least, a very strange statement in TSS:  "But like most people, I remember most things, and especially those things I'd rather forget." [13:65]

I don't know in what sense Q is talking about memory, but the first part of that statement seems indefensible (the latter part, about remembering things you'd rather forget, seems quite reasonable).  It may be he is talking about some deep level of remembering at which every experience makes its mark, whether it can be recalled consciously or not.

However, if he's talking about recalling the specifics of events, there's a rather dramatic lapse of short-term memory in this very mission.  It occurs when Q is thinking to himself, on being led out of Schrenk's apartment to be executed by Ignatov, that Schrenk's not sending Misha out of the room is "slightly short on good taste," and then wondering where he'd heard that statement before. [15:142]  Q...hel-lo?  You heard it from Schrenk, in the apartment from which you are now leaving, all of, oh, thirty minutes ago:  "It worried me, you see. I mean, it's like having one of our prisons with its execution chamber right across the street from Harrod's. Could only happen in Moscow, couldn't it? Typically Russian—slightly short on good taste." [14:98]

Perhaps, given what Schrenk has just done to him, we can forgive Q his lapse of memory, even though that would surely qualify as something Quiller would rather forget.