E=mc^2 is not wrong. There are two kinds of energy, potential energy and kinetic energy. (actually there are more kinds, like caloric energy, but that's not relevant) An apple hanging in a tree has potential energy based on the force of gravity exerted on it, and the distance to the ground. As the apple falls to the ground, that potential energy gets converted into kinetic energy, and the law of conservation of energy says that potential energy and kinetic energy are equal. You have force = mass x acceleration and work = mass x distance, and the conversion factor between force and work is velocity squared, so the kinetic energy exerted in moving the apple from the tree to the ground is the mass x velocity squared.

In terms of kinetic energy E=mc^2 is correct. The E^2 version is the potential energy version, which is actually a more useful version, but both are correct.