  We study the effect of imperfect subtraction of the Sunyaev-Zel'dovich effect
(SZE) using a robust and non-parametric method to estimate the SZE residual in
the Planck channels. We include relativistic corrections to the SZE, and
present a simple fitting formula for the SZE temperature dependence for the
Planck channels. We show how the relativistic corrections constitute a serious
problem for the estimation of the kinematic SZE component from Planck data,
since the key channel to estimate the kinematic component of the SZE, at 217
GHz, will be contaminated by a non-negligible thermal SZE component. The
imperfect subtraction of the SZE will have an effect on both the Planck cluster
catalogue and the recovered CMB map. In the cluster catalogue, the relativistic
corrections are not a major worry for the estimation of the total cluster flux
of the thermal SZE component, however, they must be included in the SZE
simulation when calculating the selection function and completeness level. The
power spectrum of the residual at 353 GHz, where the intensity of the thermal
SZE is maximum, does not contribute significantly to the power spectrum of the
CMB. We calculate the non-Gaussian signal due to the SZE residual in the 353
GHz CMB map using a simple Gaussianity estimator, and this estimator detects a
4.25-sigma non-Gaussian signal at small scales, which could be mistaken for a
primordial non-Gaussian signature. The other channels do not show any
significant departure from Gaussianity with our estimator.
