Consequences of factoring and discrete log in $P/Poly$
There appear to be pretty much no interesting consequences, from a complexity-theoretic perspective.  See Consequences of Factoring being in P? on CSTheory.  (Any consequence of factoring being in P/poly would also be a consequence of factoring being in P; but as the answers to that question state, there are basically no known complexity-theoretic consequences to factoring being in P.)

A Google search for "consequences of factoring in P/poly" also turns up Factoring Could be Easy.