I consider several problems of the evolution of the solar nebula, the precipitation of dust particles toward its central plane, and the possibility that a gravitational instability developed in the dust subdisk. A solution of the dispersion equation is given for the development of an instability in a two-component (gas-dust) rotating disk under the assumption that there is no instability in the gaseous component. This solution is compared to one found earlier for one-component disks. I emphasize that a monodisperse "initial" state with equal kilometer-sized bodies, as traditionally assumed in many numerical simulations, never existed. I note that turbulence induced by the gradient of the rotation velocity dω/ dz and differential radial drift of particles having different sizes in the gas does not exclude the possibility of a gravitational instability in a thin equatorial layer of the subdisk which contains a small fraction of the total dust mass. A runaway scenario for the accumulation of preplanetary bodies is discussed. I find that a transition to higher relative velocities of bodies and a slower growth of planet embryos began already before the sum of masses of the embryos reached one-tenth the mass of all the other bodies. Mechanisms for removal of almost all the initial mass of solids from the asteroidal zone are considered. A reliable mechanism for the sweeping out of this zone by bodies which penetrate from Jupiter's zone could work efficiently at values of the velocity parameter θ ≲ 30-50, once Jupiter's embryo reached a mass of ∼5-10 M⊕. Also at such moderate values of θ the outer planets ejected planetesimals into the cometary cloud.