  We consider four-dimensional Higher-Spin Theory at the first nontrivial order
corresponding to the cubic action. All Higher-Spin interaction vertices are
explicitly obtained from Vasiliev's equations. In particular, we obtain the
vertices that are not determined solely by the Higher-Spin algebra structure
constants. The dictionary between the Fronsdal fields and Higher-Spin
connections is found and the corrections to the Fronsdal equations are derived.
These corrections turn out to involve derivatives of arbitrary order. We
observe that the vertices not determined by the Higher-Spin algebra produce
naked infinities, when decomposed into the minimal derivative vertices and
improvements. Therefore, standard methods can only be used to check a rather
limited number of correlation functions within the HS AdS/CFT duality. A
possible resolution of the puzzle is discussed.
