It really depends on what has cropped up and how you want to present it. Those words have slightly different nuances: "mishap" sounds as if an accident or blunder has occurred; "setback" sounds as if a significant problem has delayed a project, for example, while "hitch" feels more minor. Traditionally, a sentence such as "Due to a setback/mishap/hitch, we have postponed the meeting" would be considered an incorrect use of "due to".
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.