We report on a study of the time-dependent rate of decay for the process B0 -> D(*)pi and for the process B0 -> J/psi K*0 in a data sample of about 88 million B0-B0bar meson pairs collected with the BaBar detector at the PEP II collider at SLAC. The decay channel B0 -> D(*)pi can be used to extract the CP violation parameter sin(2beta+gamma). We report the first experimental limit on |sin(2beta+gamma)| using fully reconstructed B0 -> D(*)pi events and present the constraint from this measurement on the CKM-unitarity triangle. For B0 -> J/psi K*0 we search for a deviation in the B decay-time distributions from usual B0-B0bar oscillations. Such a deviation would be an indication for a wrong-flavor decay amplitude B0 -> J/psi K^*0bar and a sign for new physics. The result can be used to put a limit on the potential difference between the measured values of sin(2beta) using B0/B0bar -> J/psi KS and B0/B0bar -> J/psi KL decays.