Remember that time River Song made a Dalek say mercy three times before she killed it? Neither does Steven Moffat.
The Doctor wasn’t there when that River made that Dalek beg for mercy in ‘The Big Bang’. He never heard it. The first time he ever heard a Dalek beg for mercy was in ‘The Witch’s Familiar’. After which he went back in time and saved Davros so that the Daleks would have a concept of mercy. Which is how that Dalek was able to beg River for mercy.
So there, not a plot hole at all.
It actually makes that scene in The Big Bang more disturbing, when you consider that it wasn’t just a word, a plea for survival, but that somewhere, beyond it, there was the concept of mery. That Dalek, somewhere within its very DNA had a genuine if diluted understanding of compassion and that’s what it begged for.
And River made it repeat it a couple of times and then shot it dead.