Don't expect Batman v Superman: Dawn of Justice to address any of the problems you had with Man of Steel.
Henry Cavill, who is reprising his role as Superman/Clark Kent in Batman v Superman, spoke with Cineplex recently and explicitly stated that they will move on with the story and not bother confronting any problems people may have had with Man of Steel.
"The reception of my first Superman movie, from what I've read, was fairly mixed. Everyone I've spoken to enjoyed the movie, but [not] unlike if you're going to meet a stranger in the street, they're not going to badmouth you to your face," Cavill said. "There's no intentional move, I don't think, in Batman v Superman to address any issues that people had with Man of Steel. It's just a continuation of that storyline and they continue to develop that world and introduce new characters."
SPOILER ALERT FOR MAN OF STEEL AHEAD:
One common complaint people had with Man of Steel was with the ending. The film concluded with Superman partially destroying Metropolis and ultimately killing General Zod (Michael Shannon). Superman has traditionally been known as a superhero that does not kill. Additionally, the movie's bleak overtones have been seen as incongruous with the usual Superman story.
However, at the end of the day, this is director Zack Snyder's interpretation of the legendary DC character--one that we haven't seen before on film. It remains to be seen how the DC Cinematic Universe will reinterpret classic stories from the comics.
Batman v Superman: Dawn of Justice is scheduled for release in theaters on March 25, 2016.