  We investigate the use of estimators of weak lensing power spectra based on a
flat-sky implementation of the Pseudo-Cl (PCl) technique, where the masked
shear field is transformed without regard for masked regions of sky. This
masking mixes power, and E-convergence and B-modes. To study the accuracy of
forward-modelling and full-sky power spectrum recovery we consider both
large-area survey geometries, and small-scale masking due to stars and a
checkerboard model for field-of-view gaps. The power spectrum for the
large-area survey geometry is sparsely-sampled and highly oscillatory, which
makes modelling problematic. Instead, we derive an overall calibration for
large-area mask bias using simulated fields. The effects of small-area star
masks can be accurately corrected for, while the checkerboard mask has
oscillatory and spiky behaviour which leads to percent biases. Apodisation of
the masked fields leads to increased biases and a loss of information. We find
that we can construct an unbiased forward-model of the raw PCls, and recover
the full-sky convergence power to within a few percent accuracy for both
Gaussian and lognormal-distributed shear fields. Propagating this through to
cosmological parameters using a Fisher-Matrix formalism, we find we can make
unbiased estimates of parameters for surveys up to 1,200 deg$^2$ with 30
galaxies per arcmin$^2$, beyond which the percent biases become larger than the
statistical accuracy. This implies a flat-sky PCl analysis is accurate for
current surveys but a Euclid-like survey will require higher accuracy.
