In which works by Somerset Maugham is mild humor noted?
Though his best known works of fiction are quite serious in tone and intent, there are quite a number of Maugham's works that contain mild humor.
For example, in The Razor's Edge, the portrait of Elliot is not outright funny, but it is definitely tongue in cheek (with how extreme his clothing is, and how silly he is). Likewise, Gray is so much a living cliche that one can't help but smile at him, and Isabel gets off a few good lines.
The sketches of the social scene in The Moon and Sixpence are good quiet satire. Maugham is very aware of how aware people are of the rules and prestige of the social scene.
However, if you really want to see Maugham's sense of humor at its best, you should look into his plays, like "The Bread-Winner." It satirizes both established standards and changes due to feminism, and can be quite funny.