We knew that Rachel was successful, so we can rule out ineptitude. We also know that she had a certain engagement with her errors. This suggests impeccability over resilience as a good choice for the first blank. If she was convinced of her own impeccability (flawlessness) , she would not notice her errors, thus discerned is the right choice for the second blank.

But doesn't not noticing something mean you're overlooking it? Can you explain the reason for eliminating overlook over discern? Much appreciated!

Overlooked means when you do not pay attention carefully. In this case to the errors

Discern means she did not differentiate. She was not able to understand what was wrong and what was right because she was too convinced of herself. A house self esteem