We present results of a search for D0-D(-)0 mixing and a measurement of R(D), the ratio of doubly Cabibbo-suppressed decays to Cabibbo-favored decays, using D0-->K+pi- decays from 57.1 fb(-1) of data collected near sqrt[s]=10.6 GeV with the BABAR detector at the PEP-II collider. At the 95% confidence level, allowing for CP violation, we find the mixing parameters x('2)<0.0022 and -0.056<y(')<0.039, and the mixing rate R(M)<0.16%. In the limit of no mixing, R(D)=[0.357+/-0.022(stat)+/-0.027(syst)]% and the CP-violating asymmetry A(D)=0.095+/-0.061(stat)+/-0.083(syst).