  We perform a detailed study of the various one-loop contributions leading to
production of the Standard Model Higgs boson in association with a hard jet.
This production mode contributes to the current Tevatron exclusion limit of the
Standard Model Higgs with 160 GeV < M_H < 170 GeV, and will also be important
for discovery and interpretation of new scalar bosons at the Large Hadron
Collider (LHC). We include top- and bottom-quark initiated contributions,
maintaining the exact dependence on the quark masses, and also study previously
neglected W- and Z-boson mediated effects which shift the qg and q\bar{q}
production modes. We consider the deviations from commonly used approximations
for the Higgs boson transverse momentum spectrum caused by the finite top-quark
mass, bottom quark contributions, and electroweak gauge boson terms. All three
effects act to decrease the Higgs boson transverse momentum distribution for
observable momenta, with shifts reaching -8% at the Tevatron and -30% at the
LHC. The shifts have a significant dependence on the Higgs p_T, and are
especially important if large momenta are selected by experimental cuts.
