We explore the relationship between features in the Planck 2015 temperature and polarization data, shifts in the cosmological parameters, and features from inflation. Residuals in the temperature data at low multipole $ell$, which are responsible for the high $H_0approx 70$ km s$^{-1}$Mpc$^{-1}$ and low $sigma_8Omega_m^{1/2}$ values from $ell<1000$ in power-law $Lambda$CDM models, are better fit to inflationary features with a $1.9sigma$ preference for running of the running of the tilt or a stronger $99%$ CL local significance preference for a sharp drop in power around $k=0.004$ Mpc$^{-1}$ in generalized slow roll and a lower $H_0approx 67$ km s$^{-1}$Mpc$^{-1}$. The same in-phase acoustic residuals at $ell>1000$ that drive the global $H_0$ constraints and appear as a lensing anomaly also favor running parameters which allow even lower $H_0$, but not once lensing reconstruction is considered. Polarization spectra are intrinsically highly sensitive to these parameter shifts, and even more so in the Planck 2015 TE data due to an outlier at $ell approx 165$, which disfavors the best fit $H_0$ $Lambda$CDM solution by more than $2sigma$, and high $H_0$ value at almost $3sigma$. Current polarization data also slightly enhance the significance of a sharp suppression of large-scale power but leave room for large improvements in the future with cosmic variance limited $E$-mode measurements.
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