What is the significance of Meursault not caring for important events like his mother's death in "The Stranger"? Why does he notice small details like the scabs on the dog?
This aspect of Meursualt's personality is one of the main themes in the story. The absurdity of his emotional indifference to serious events cause Meursault to reflect on the meaninglessness of a person's life in society. Meursault refuses to consider anything such as fate or God as a reason for man's actions and existence. He can only use logic. Whether it is his mother's death, Marie's need to prove his love for her, or even his killing a man, nothing actually penetrates his emotional core. Yet, he pays attention to details, such as the scabs on the dog, because they are no threat to his emotional isolation.
This punctuates his complete disregard for proper behavior and for the thoughts and feelings of others. It also focuses our attention on Meursault's shocking apathy. He doesn't care for anything, including the death of his own mother.
I think Mersault does care about his mother's death, he just doesn't show the emotions that one would expect a man to show in the wake of the death of his mother. He says a few times that he probably loved his mother a great deal, but that that didn't mean anything. He also thinks about his mother when Salamono weeps for his lost dog.
Mersault doesn't care for any events as such, he is only interested in the physical side of life, emotions are not important and merely prevent you from living your life. The scabs on the dog are a physical characteristic while his mothers death is supposed to trigger an emotional response.
Camus is concerned with presenting the reader with a character whose indifference is his characterising feature. The most prominent issue within the book is Meaursault's highly unconventional approach to death. The way in which he deals with his mother's funeral, the murder and his own imprisonment is through a detached and absurd perspective. It serves to aid Camus' overarching existential approach to the work - in that he questions the very meaning of what may seem like such mundane and banal events.
When writing an essay which focuses upon this aspect of the book, you might like to question whether he does 'care' for the death of his mother. For example, you might take a psychological reading of the book and associate the death of his mother to the chain of events which eventually lead to his 'downfall' (you may even question this).