How one deals with wrong notes depends on what one is trying to accomplish.

When learning a new piece, it is useful to distinguish between the different skills needed.

“HARD, HIGH-PRECISION SKILLS are actions that are performed as correctly and consistently as possible, every time. They are about repeatable precision. It helps to be careful, slow, and keenly attuned to errors because the first reps establish the pathway for the future.  

SOFT, HIGH-FLEXIBILITY SKILLS aren’t about doing the same thing perfectly every time, but rather about being agile and interactive. With these skills, we are not trying for Swiss-watch precision, but rather for the ability to quickly recognize a pattern or possibility, and to work past a complex set of obstacles. Soft skills are built by playing and exploring.”

(from Daniel Coyle “The Little Book of Talent – 52 Tips for Improving your Skills”) 

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The HARD SKILL, as it pertains to learning a new piece, especially the notes, is:

• repeatable precision, getting it right the first time and every time, no pecking at the keys until it sounds like it could be correct. 
  • Frances Clark says, “We must rid ourselves of the notion that in each day of practice, we make fewer mistakes than the day before. Practice is playing perfection again and again.“

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To succeed, one must figure out what it takes to get it right the first time and every time.

Examples are:

1. writing note names, finger numbers and counting in the score;

• • how to know which note names to write in the score: use the two-second rule: if it takes two seconds or longer to name the note and/or find the key on the piano – write the note name in the score.
  • Stephen Hough says, “When starting to learn a piece I always write in fingerings. It aids memory, it emphasises the act of study, it discourages a sloppy “sight-read till ready” attitude, it forestalls nerves in a performance, it personalises the score.”

2. circling easy-to-overlook details such as sharps and flats from the key signature, accidentals;

3. but most importantly: abandoning fluency and GOING SLOW and DELIBERATE.

1. • Stephen Hough says, “Slow practice can be a complete waste of time if the mind is not working quickly. Simply to trawl through passages like a contented tortoise is a waste of the felt on your piano’s hammers. Good slow practice is more like a hare pausing to survey the scene sharp in analysis, watching through the blades of grass, calculating the next sprint. […] It stops any tortoisian ambling and it focuses the mind quickly from one reflex to another. It is a hare with alert eyes.”
   • Madeline Bruser says, “The real key to vivid engagement with music isn’t slowness. It’s attention. But most of us are so used to speeding through all of our activities, including our practicing, that we need to slow down a lot at first in order to discover the power of attention. As we develop our listening capacity much more, it operates fully at faster and faster speeds.”
   • Diane Hidy says, “Practice at the speed of no mistakes.”
   • Someone else said, “Do yourself a favor and get it right!”

These tactics are like a cast for a broken bone:

They are necessary for success (healing a broken bone without a cast is possible but not likely to yield desirable results), and

They are temporary (cast comes off when the bone is healed). It is helpful to make a copy of the score to initially write note names, fingerings, helpful comments in the score, and then as one progresses set that copy aside and make a new one for a new set of comments and helpful hints.

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SOFT SKILLS, as they pertain to learning to play a piece, have to do with exploring, experimenting with vague details such as pedal and dynamics, etc. = there is no one correct way.

Here, it is ok to ignore an accidental wrong note, especially if fluency is the goal.

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Hard skills build the house, soft skills apply wallpaper. You can – you probably should! – dream  about wallpaper while the house is being built but you cannot apply it until you have walls.