Theoretical corrections on scalar gravitational waves

Following some ideas in the Landau book, some corrections about errors in the old literature on scalar gravitational waves are given and discussed. Even if such errors can be considered not important from the point of view of observations, because they do not alter the interferometric response function for scalar gravitational waves, the presented analysis is due and very important for a sake of completeness and for a better understanding of the linearized theory of Scalar-Tensor Gravity