We present the results of a Dalitz plot analysis of D^0 to K^0_S pi^0 pi^0 using the CLEO-c data set of 818 inverse pico-barns of e^+ e^- collisions accumulated at sqrt{s} = 3.77 GeV. This corresponds to three million D^0 D^0-bar pairs from which we
select 1,259 tagged candidates with a background of 7.5 +- 0.9 percent. Several models have been explored, all of which include the K^*(892), K^*_2(1430), K^*(1680), the f_0(980), and the sigma(500). We find that the combined pi^0 pi^0 S-wave contribution to our preferred fit is (28.9 +- 6.3 +- 3.1)% of the total decay rate while D^0 to K^*(892)^0 pi^0 contributes (65.6 +- 5.3 +- 2.5)%. Using three tag modes and correcting for quantum correlations we measure the D^0 to K^0_S pi^0 pi^0 branching fraction to be (1.059 +- 0.038 +- 0.061)%.
We have searched for flavor-changing neutral current decays and lepton-number-violating decays of D^+ and D^+_s mesons to final states of the form h^+- e^-+ e^+, where h is either pi or K. We use the complete samples of CLEO-c open-charm data, corres
ponding to integrated luminosities of 818 pb^-1 at the center-of-mass energy E_CM = 3.774 GeV containing 2.4 x 10^6 D^+D^- pairs and 602 pb^-1 at E_CM = 4.170 GeV containing 0.6 x 10^6 D^*+-_s D^-+_s pairs. No signal is observed in any channel, and we obtain 90% confidence level upper limits on branching fractions B(D^+ --> pi^+ e^+ e^-) < 5.9 x 10^-6, B(D^+ --> pi^- e^+ e^+) < 1.1 x 10^-6, B(D^+ --> K^+ e^+ e^-) < 3.0 x 10^-6, B(D^+ --> K^- e^+ e^+) < 3.5 x 10^-6, B(D^+_s --> pi^+ e^+ e^-) < 2.2 x 10^-5, B(D^+_s --> pi^- e^+ e^+) < 1.8 x 10^-5, B(D^+_s --> K^+ e^+ e^-) < 5.2 x 10^-5, and B(D^+_s --> K^- e^+ e^+) < 1.7 x 10^-5.
