In this dissertation we describe several technical developments for extracting cosmological information from and controlling systematic errors in weak lensing surveys. We propose a method to constrain photometric redshift error distributions using galaxy angular cross correlation functions. This is a form of "self-calibration" of galaxy clustering data that allows better knowledge of the mean redshift errors produced by a given photometric redshift estimation code. No spectroscopic training samples are required, which makes this method an important complement to existing calibration techniques. We forecast the photo-z error constraints possible using only our method with the LSST and find that additional constraints are required to meet the survey targets. We also describe a statistical framework for using a select number of cosmological simulations in performing parameter inference from tracers of the matter power spectrum. Computational barriers are often met when theoretical predictions of the data must be computed via simulations or when the distribution of errors on the data is unknown. Our framework addresses both of these issues to allow accurate parameter constraints with a computationally feasible number of simulations of the data. We demonstrate the performance of this algorithm using a two-parameter toy model for the matter power spectrum.