We study the effect of electronic interactions on the addition spectra and on the energy-level distributions of two-dimensional quantum dots with weak disorder using the self-consistent Hartree- Fock approximation for spinless electrons. We show that the distribution of the conductance peak spacings is Gaussian with large fluctuations that exceed, in agreement with experiments, the mean level spacing of the noninteracting system. We analyze this distribution on the basis of Koopmans' theorem. We show furthermore that the occupied and unoccupied Hartree-Fock levels exhibit Wigner-Dyson statistics.