When we consider the character of Mr. White in this masterful horror story the first characteristic that we are presented with is a negative trait in his personality. Consider how, in the first paragraph, Mr. White's style of playing chess is presented:
Father and son were at chess, the former, who possessed ideas about the game involving radical changes, putting his king into such sharp and unnecessary perils...
It appears, then, that Mr. White is a risk-taker and is not scared of going against convention. Note how this effectively foreshadows his first use of the monkey's paw.
If you are looking for a positive trait it would definitely have to be his quick understanding of what he has unleashed with his second wish and what precisely is knocking at the door. His quick-thinking enables him to use the third wish and protect both him and his wife from the cadaver that awaits them.