What specifically is incorrect about the Dirac Sea interpretation?

So taking the square root of $E^2 = (m_oc^2)^2 + p^2c^2$ yields two solutions.

The Dirac Sea treats the negative solution as an infinite space of electrons with negative energy.

All the observable electrons have positive energies. As an electron lose energy, another electron somewhere else in the universe gains energy, so that the total positive energy is balanced with the negative energy.

Seems to be a good explanation I can use for explaining the negative part of the Energy-Mass equivalence. What is it about this interpretation that people disagree with?

The Dirac sea interpretation cannot deal with bosonic antiparticles. At the time it was conceived, I don't think physicists were aware that antibosons existed. A simple example of a boson-antiboson pair are the $W^\pm$ bosons. In order to prevent an electron from falling into a negative energy state, we use the Pauli principle. A fermion cannot fall into a fully occupied sea of other fermions. This obviously does not apply to bosons.