We consider various tests of the lattice cluster theory to ascertain its range of applicability. We investigate this theory by applying it to an incompressible binary system. All versions of the theory predict a spurious phase separation and an associated critical point(s) in the miscible region. Higher than second-order versions also predict two nearby but distinct critical points for phase separation in the immiscible region. Various other problems are also discovered. All these problems are present when the theory is applied to other systems also, thus severely restricting the predictability and the reliability of the theory.