Continuity mistake: When Batman goes to save Martha, he pulls the wooden box with his gun and throws it at one bad guy. The guy's head hits the wall, leaving blood. Later on, you still can see the dead guy but there is no blood on the wall any more. The blood appears again when Batman is about to finish off the last person who was stabbed and pinned against the wall. (02:17:30 - 02:18:35)
Continuity mistake: Superman gets his hair messed up during his fight with Batman, but while he is fighting Doomsday his hair is perfectly combed again.
Continuity mistake: After the mercenaries kill everyone in the desert, there are two guys looking at them using two monitors. The pencil below them changes from white to blue.
Continuity mistake: When Perry asks Clark to do the sports note he has the paperwork in his left hand but in the next shot he is holding it in his right.
Continuity mistake: In the beginning, Bruce Wayne drives his car towards all the chaos, but the crowd is too thick for him and his car to get through, but with movie magic suddenly Bruce and his car are at the front of the crowd. (00:07:00)
Continuity mistake: After Batman shots the tracking device onto the truck, later in the warehouse the device is next to a number 5 that was not there before.
Chosen answer: The beginning is Bruce Wayne's perspective of the events that occurred in the movie "Man of Steel" when Superman and General Zod are fighting (if you haven't seen it, it would explain a lot of BvS events). It's General Zod's ship and the phantom drive. It cuts to 18 months later. Supermen is called to testify in front of a congressional hearing because of his vigilantism over the past 18 months and people are concerned about his actions (like the events in Africa) since he's an all-powerful alien with no way for the people to stop him, so they're very nervous. Bruce seems to blame Superman more than anyone though for the destruction and death of people he knew (and tried to save) because if Superman wasn't on Earth, Zod wouldn't have come to Earth, etc.
Bishop73