We investigate the weak lensing corrections to the cosmic microwave background temperature and polarization anisotropies. We consider all the effects beyond the leading order: post-Born corrections, LSS corrections, and, for the polarization anisotropies, the correction due to the rotation of the polarization direction between the emission at the source and the detection at the observer. We show that the full next-to-leading order correction to the B-mode polarization is not negligible on small scales and is dominated by the contribution from the rotation; this is a new effect not taken into account in previous works. Considering vanishing primordial gravitational waves, the B-mode correction due to rotation is comparable to cosmic variance for $\ell \gtrsim 3500$, in contrast to all other spectra where the corrections are always below that threshold for a single multipole. Moreover, the sum of all the effects is larger than cosmic variance at high multipoles, showing that higher-order lensing corrections to B-mode polarization are in principle detectable.

We present two new covariant and general prescriptions for averaging scalar observables on spatial regions typical of the observed sources and intersecting the past light-cone of a given observer. One of these prescriptions is adapted to sources exactly located on a given space-like hypersurface, the other applies instead to situations where the physical location of the sources is characterized by the experimental "spread" of a given observational variable. The geometrical and physical differences between the two procedures are illustrated by computing the averaged energy flux received by distant sources located on (or between) constant redshift surfaces, and by working in the context of a perturbed ΛCDM geometry. We find significant numerical differences (of about ten percent or more, in a large range of redshift) even limiting our model to scalar metric perturbations, and stopping our computations to the leading non-trivial perturbative order.