  The Lorentz covariant all-loop counterterms built in the 4+32 on shell
superspace of N=8 supergravity imply that the theory is not UV finite.
Meanwhile, the relevant counterterms depending on the light-cone superfields in
4+16 superspace have not been constructed so far. Our first attempt to
construct them suggests that they may be incompatible with the covariant ones.
This would lead to a prediction of all-loop UV finiteness of the perturbative
S-matrix. Here we rely on the validity of the equivalence theorem for the
S-matrix in the light-cone gauge and Lorentz covariant gauges, which requires
the absence of BRST anomalies. We discuss the status of N=8 SU(8) and E7
anomalies. It remains an outstanding problem to construct the light-cone
counterterms or to confirm our current conclusion.
