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...

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.