On the Roman planet in "Bread and Circuses", Captain Kirk is given a a slave woman for a night, who even goes so far as to say that Kirk "owns" her for the night. While he is initially hesitant because he thinks it is a trap, he eventually responds to her advances, the camera pans up from his bed, and the scene fades to morning with Kirk alone.
Are we to believe that Kirk had intimate sexual relations with a woman that considered herself his slave? I have trouble believing this, since it would make Kirk look like a hypocrite, as in the very same episode he emphatically defended both the Prime Directive and the Federation's lack of slavery.