We know from the successful experiments demonstrating Bell's inequality and entanglement that the universe is not classical, but quantum mechanical. This means that it behaves in very non-intuitive ways. The "measurement problem" arises because we can't formulate a good intuitive picture of what's going on. One way that we try to explain it, the "Copenhagen interpretation," makes calculations relatively easy, but has a mysterious step, "measurement," which eludes our intuition. Explaining this measurement step is known as the "measurement problem," and since it is fundamentally a problem with our intuition, there may be no solution (note that adherents of the many-worlds interpretation and the de Broglie-Bohm pilot-wave interpretation claim to have solved the measurement problem, but in each case they have replaced it with something equally abhorrent to our intuitions).

For a theory of everything, there are two possibilities. The first is that it's still fundamentally quantum mechanical, in which case the situation will remain much the same and the measurement problem will not go away. The second is that it is fundamentally something other than quantum mechanical. Because it still has to approximate quantum mechanics, it's not going to behave according to our classical intuition. I think this means that it would very likely be even more non-intuitive than quantum mechanics, and the measurement problem would be replaced by something even more difficult to understand.

We know from the successful experiments demonstrating Bell's inequality and entanglement that the universe is not classical, but quantum mechanical. This means that it behaves in very non-intuitive ways. The "measurement problem" arises because we can't formulate a good intuitive picture of what's going on. One way that we try to explain it, the "Copenhagen interpretation," makes calculations relatively easy, but has a mysterious step, "measurement," which eludes our intuition. Explaining this measurement step is known as the "measurement problem," and since it is fundamentally a problem with our intuition, there may be no solution (note that adherents of the many-worlds interpretation and the de Broglie-Bohm pilot-wave interpretation claim to have solved the measurement problem, but in each case they have replaced it with something equally abhorrent to our intuitions).

Quantum mechanics isn't just a theory of the universe, but really a framework used for constructing all sorts of theories (the Standard model, string theory, non-relativistic quantum mechanics). For a theory of everything, there are two possibilities. The first is that it's still fundamentally quantum mechanical, in which case the situation will remain much the same and the measurement problem will not go away. The second is that it is fundamentally something other than quantum mechanical. Because it still has to approximate quantum mechanics, it's not going to behave according to our classical intuition. I think this means that it would very likely be even more non-intuitive than quantum mechanics, and the measurement problem would be replaced by something even more difficult to understand.