What is the meaning of the line “A mediæval doctor would have called him saturnine”?

Medieval doctors believed that those who are born when Saturn is rising in the sky may tend toward solemn dispositions. Here, Joyce means that Mr. Duffy is a gloomy person.

Why is Mr. Duffy so affected by the lovers in the park at the end of the story?

After learning of Mrs. Sinico’s death, Mr. Duffy mourns the only real companion he ever had. He is jealous and saddened by the lovers that he passes in the park on the way home because he feels that he will never have that type of a relationship with anyone now that Mrs. Sinico is gone.

Why is Mrs. Sinico’s husband okay with Mr. Duffy’s frequent presence at the Sinico estate?

Mr. Sinico thinks that Mr. Duffy might eventually ask to marry their daughter. He is also often away from home when these visits occur because he is a captain of a mercantile boat. 

Why are there so many references to music in “A Painful Case”?

Music is a motif throughout Dubliners and is featured in many of the short stories including “The Dead,” “Eveline,”  “Two Gallants,” and “The Boarding House.” The repeated references to music throughout Dubliners provide a glimpse into Ireland’s rich musical tradition and immerses the reader in Irish culture.

What is the “Rotunda”?

The Rotunda’s full name is The Rotunda Concert Hall and it is a real concert hall in Dublin. In the context of “A Painful Case,” it is where Mr. Duffy first runs into Mrs. Sinico and her daughter.