  Let $\mathcal{M}_g$ be the moduli space of hyperbolic surfaces of genus $g$
endowed with the Weil-Petersson metric. In this paper, we show that for any
$\epsilon>0$, as $g\to \infty$, for a generic surface in $\mathcal{M}_g$, the
error term in the Prime Geodesic Theorem is bounded from above by $g\cdot
t^{\frac{3}{4}+\epsilon}$, up to a uniform constant multiplication. The
expected value of the error term in the Prime Geodesic Theorem over
$\mathcal{M}_g$ is also studied. As an application, we show that as $g\to
\infty$, on a generic hyperbolic surface in $\mathcal{M}_g$ most closed
geodesics of length significantly less than $\sqrt{g}$ are simple and
non-separating, and most closed geodesics of length significantly greater than
$\sqrt{g}$ are not simple, which confirms a conjecture of Lipnowski-Wright.
  A novel effective upper bound for intersection numbers on $\mathcal{M}_{g,n}$
is also established, when certain indices are large compared to $\sqrt{g+n}$.
