Is it obligatory to condemn evil if it is manifest without spying, such as backbiting aloud or mispronouncing a letter in Quranic recitation?

If you are in one place, and the sound of backbiting is audible to those in the classroom or on the chair, then this is not considered spying. In this case, the one who hears it must denounce the evil. As for correcting the mistake of the student who is reciting to her teacher, you are not obligated to correct her mistake. It is preferable to leave the correction to her teacher, for perhaps she sometimes refrains from alerting her to her mistake out of kindness to her and to avoid alienating her.