  It has recently been pointed out that viable sparticle mass spectra can be
generated in Yukawa unified SO(10) supersymmetric grand unified models
consistent with radiative breaking of electroweak symmetry. Model solutions are
obtained only if $\tan\beta \sim 50$, $\mu <0$ and positive $D$-term
contributions to scalar masses from SO(10) gauge symmetry breaking are used. In
this paper, we attempt to systematize the parameter space regions where
solutions are obtained. We go on to calculate the relic density of neutralinos
as a function of parameter space. No regions of the parameter space explored
were actually cosmologically excluded, and very reasonable relic densities were
found in much of parameter space. Direct neutralino detection rates could
exceed 1 event/kg/day for a $^{73}$Ge detector, for low values of GUT scale
gaugino mass $m_{1/2}$. We also calculate the branching fraction for $b\to s
\gamma$ decays, and find that it is beyond the 95% CL experimental limits in
much, but not all, of the parameter space regions explored. However, recent
claims have been made that NLO effects can reverse the signs of certain
amplitudes in the $b\to s\gamma$ calculation, leading to agreement between
theory and experiment in Yukawa unified SUSY models. For the Fermilab Tevatron
collider, significant regions of parameter space can be explored via
$b\bar{b}A$ and $b\bar{b}H$ searches. There also exist some limited regions of
parameter space where a trilepton signal can be seen at TeV33. Finally, there
exist significant regions of parameter space where direct detection of bottom
squark pair production can be made, especially for large negative values of the
GUT parameter $A_0$.
