The key to Miss Marple's sleuthing is her insight into human behavior. Regardless of the violent act that has occurred, there is a simple, human reason/motivation behind it. By observing people and comparing those observations to other observations of human behavior in her history (which Miss Marple has quite a store of....), Miss Marple manages to click all the pieces into place.
I think the key word is "observant." -- Note the use of the word over and over again in the above paragraph. =)
The whole reason readers want to follow Miss Marple's mysteries is her skill at observing things. It's a trait she shares with Poirot, though her style of observation is more relateable, in my opinion. It indicates that the only thing keeping us everyday folk out of the sleuthing world is the ability to pay attention.
Regardless of genre, I think readers appreciate a character who can pay attention. As a reader, I certainly don't like spending time with a character who is navel-gazing or whining and, all the while, this other, more interesting stuff is going on. I think that kind of behavior makes an unlikeable character.