During Clark Kent and Bruce Wayne's (rather tense) conversation, Clark's seen standing in front of a painting that appears to be a work by artist Cleon Peterson. This in and of itself isn't necessarily news, as Peterson has said publicly that some of his art will be seen hanging at Lex Luthor's pad. But the painting in question, titled A Balance of Terror, seems hugely significant. The theme of the work, which depicts the casual, senseless slaughter of one group of people by another, is that absolute power corrupts absolutely—that those who possess it are essentially doomed to destroy those who do not.
That point of view directly reflects Batman's reasons for worrying about Superman's presence on Earth, as well as echoing words said by Luthor in the trailer. The painting's black-and-white color scheme also encapsulates our heroes' opposing points of view. Superman, on the light side, seeks to help the helpless; conversely, Batman seeks out the dark, where he can root out evil before it has a chance to destroy. Whether any of this is stated explicitly in Batman v Superman: Dawn of Justice, the painting's presence in the film would seem to reflect some impressively layered thinking on the part of screenwriters David S. Goyer and Chris Terrio.