What is the secret of successful practise? Don't play the wrong notes! Does that sound simplistic? Bear with me.
I auditioned a few years back to be an ABRSM examiner (they didn't take me, after it emerged that I couldn't listen and write at the same time, which was something I didn't know about myself). Anyway, there was a Grade 8 singing candidate who messed up the sight-reading. She knew, of course, because she was very good. I offered a second go, and in my naivety was really surprised that it was pretty much exactly the same.
I've since found that this is common - even when people know something is wrong, they will sing or play it wrong again.
Hence the mantra (well, my mantra!) "You need to play that again, not because it is wrong, but because it is right". Students need repetition to get things right, and then they need more repetition to keep them right. Repeticio est Mater Studiorum!
Here's what I've learned: when you play or sing wrong notes the brain learns them - it is almost as if the brain is undiscriminating, saying to itself "That's how s/he played it the last time, that must be how it goes; I'll do it again that way". This might have been helpful 100,000 years ago, out hunting on the plains, but it is a real problem in the piano studio.
Students are impatient, worse luck. They need to Hasten Slowly (that's another mantra!)