What details, or lack of details, does the author provide to develop the central characters in "The Monkey's Paw"?

The author leaves out detail concerning the actual wishes that Sergeant Major Morris made on the monkey's paw.  The reader has no information about what happened to his three wishes, the Sergeant Major only informs us that the first owner of the monkey's paw third wish was for death.

"Well, why don't you have three, sir?" said Herbert White cleverly.   The soldier regarded him in the way that middle age is wont to regard presumptuous youth. "I have," he said quietly, and his blotchy face whitened.  "And did you really have the three wishes granted?" asked Mrs. White.   "I did," said the sergeant-major, and his glass tapped against his strong teeth.   "And has anybody else wished?" inquired the old lady.   "The first man had his three wishes, yes," was the reply. "I don't know what the first two were, but the third was for death. That's how I got the paw." (Jacobs)

The Whites don't ask Sergeant-Major Morris what he wished for, and the only real warning that he gives them is to wish for something sensible.

Another important detail that is left out occurs after Mr. White has made his first wish for two hundred pounds, and as a result, his son Herbert is killed in an accident at the factory where he works, after Mr. White makes his second wish, for Herbert to return from the grave,

"He raised his hand. "I wish my son alive again." (Jacobs)

we never know what it is that knocks at the door, because Mrs. White does not get to answer it in time before Mr. White wishes it away.   

" There was another knock, and another. The old woman with a sudden wrench broke free and ran from the room. Her husband followed to the landing, and called after her appealingly as she hurried downstairs." (Jacobs)

The reader assumes that the person knocking on the door is Herbert returned from the grave, but we never find out because Mr. White doesn't want to find out what is knocking on his door, so he silently wishes it away.

"He heard the creaking of the bolt as it came slowly back, and at the same moment he found the monkey's paw, and frantically breathed his third and last wish." (Jacobs)

The reader doesn't find out what the third wish actually was, whether he wished his son back to the grave or just wished away whatever was knocking on the front door.