In 'The Last Leaf', an ambulance arrives ringing its bells to carry away a dead person. The ambulance also leaves while ringing its bells. In both cases, there is no emergency, and, thus, bells would not be necessary.
In the first segment, as the man who had the umbrella runs off, a shadow of the camera can be seen on Horace's back.
The third segment is supposed to take place in Greenwich Village, but the street sign indicates the location is near East 19th Street. The northern border of Greenwich Village is 14th Street. That location, though, is an Easter egg, as that's where O Henry lived and drank during his most productive late period. After a brief scene there, the action moves to Greenwich Village, where the rest of the story is set.
The bear in "Ransom of Red Chief" is a sun bear. Sun bears are native to Southeast Asia and not normally found in the state of Alabama.