  The reconstruction of the CMB lensing potential is based on a Taylor
expansion of lensing effects which is known to have poor convergence
properties. For lensing of temperature fluctuations, an understanding of the
higher order terms in this expansion which is accurate enough for current
experimental sensitivity levels has been developed in Hanson et. al. (2010), as
well as a slightly modified Okamoto and Hu quadratic estimator which
incorporates lensed rather than unlensed spectra into the estimator weights to
mitigate the effect of higher order terms. We extend these results in several
ways: (1) We generalize this analysis to the full set of quadratic
temperature/polarization lensing estimators, (2) We study the effect of higher
order terms for more futuristic experimental noise levels, (3) We show that the
ability of the modified quadratic estimator to mitigate the effect of higher
order terms relies on a delicate cancellation which occurs only when the true
lensed spectra are known. We investigate the sensitivity of this cancellation
to uncertainties in or knowledge of these spectra. We find that higher order
terms in the Taylor expansion can impact projected error bars at experimental
sensitivities similar to those found in future ACTpol/SPTpol experiments.
