  We update the theoretical predictions for the production cross sections of
the Standard Model Higgs boson at the Fermilab Tevatron collider, focusing on
the two main search channels, the gluon-gluon fusion mechanism $gg \to H$ and
the Higgs-strahlung processes $q \bar q \to VH$ with $V=W/Z$, including all
relevant higher order QCD and electroweak corrections in perturbation theory.
We then estimate the various uncertainties affecting these predictions: the
scale uncertainties which are viewed as a measure of the unknown higher order
effects, the uncertainties from the parton distribution functions and the
related errors on the strong coupling constant, as well as the uncertainties
due to the use of an effective theory approach in the determination of the
radiative corrections in the $gg \to H$ process at next-to-next-to-leading
order. We find that while the cross sections are well under control in the
Higgs--strahlung processes, the theoretical uncertainties are rather large in
the case of the gluon-gluon fusion channel, possibly shifting the central
values of the next-to-next-to-leading order cross sections by more than
$\approx 40%$. These uncertainties are thus significantly larger than the
$\approx 10%$ error assumed by the CDF and D0 experiments in their recent
analysis that has excluded the Higgs mass range $M_H=$162-166 GeV at the 95%
confidence level. These exclusion limits should be, therefore, reconsidered in
the light of these large theoretical uncertainties.
