An alert listener is someone who is attentive, watchful, and quick to notice things. Among the options, 'alert' is the only adjective that describes a state of being attentive and observant, which fits perfectly with the context of noticing an error. 'Anxious' and 'apprehensive' describe fear or worry, 'appreciable' means noticeable or significant, and 'appreciative' means showing gratitude - none of which fit as well as 'alert'.