This is a very short story, and Jacobs has a lot to do in very little time. How does he reveal which characters are trustworthy and reliable, and which ones may not be?

I think that the third person narrative gives us clues. Consider Mr.White's relationship with his son Herbert at the beginning of the story.

Mr. White seems reckless in his game of chess. He makes an impulsive move and pays the price. This represents his impulsive recklessness when dealing with the monkey paw. Mr. White is also dishonest because he tries to distract his son from the game.

Listen to the wind,’ said Mr white. He had made a serious mistake and wanted to distract his son’s attention so that he wouldn’t see it.

This dishonesty is reflected when he deals with Sergeant-Major Morris over the paw.