Synonyms for Heedlessness (same or very similar meaning)
WordNet sense 1 (a lack of attentiveness (as to children or helpless people)):
inattentivenessWordNet sense 2 (the trait of acting rashly and without prudence):
mindlessness, rashnessWordNet sense 3 (the trait of forgetting or ignoring your responsibilities):
inadvertence, inadvertency, unmindfulnessFrom the ODE community, based on WordNetadd/edit