Poor Doctor Monygham—he's described as a "bitter, eccentric character" (I.6.2) that nobody seems to like all that much. The primary exception to this appears to be Mrs. Gould, who appointed him the medical officer at the mine. It seems he's kind of a tough guy to get to close to; according to the narrator:
…no one could be on intimate terms with El Señor Doctor, who, with his twisted shoulders, drooping head, sardonic mouth, and side-long bitter glance, was mysterious and uncanny. (I.8.18)
So he's not exactly prom king.
That said, he scores points in our books for being extremely loyal to Mrs. Gould—in fact, unbeknownst to basically everyone (except the readers, naturally), he carries around some fairly deep feelings for her. He risks a great deal (like, his life) to help protect her family during the invasion of anti-Ribiera forces in Sulaco. So, that's definitely at least a few points in his column.
Continuing in the category of "Things that Give Us the Warm Fuzzies About Dr. M.": Turns out that during the reign of the tyrannical and paranoid Guzmán Bento, he was imprisoned and tortured for his role in a completely imaginary conspiracy against Bento. That would explain the limp and the twisted shoulders.
The doctor makes a bit of an effort to be a friend (or at least ally) to Nostromo when he returns to Sulaco from hiding the silver, but Nostromo doesn't trust him at all. He pretty much remains misunderstood and despised until the end of the novel, except by the Goulds.