  We use scanning tunneling microscopy to map the surface structure, nanoscale
electronic inhomogeneity, and vitreous vortex phase in the hole-doped
superconductor Sr$_{0.75}$K$_{0.25}$Fe$_2$As$_2$ with $T_c$=32 K. We find the
low-$T$ cleaved surface is dominated by a half-Sr/K termination with $1\times
2$ ordering and ubiquitous superconducting gap, while patches of gapless,
unreconstructed As termination appear rarely. The superconducting gap varies by
$\sigma/\bar{\Delta}$=16% on a $\sim$3 nm length scale, with average
$2\bar{\Delta}/k_B T_c=3.6$ in the weak coupling limit. The vortex core size
provides a measure of the superconducting coherence length $\xi$=2.3 nm. We
quantify the vortex lattice correlation length at 9 T in comparison to several
iron-based superconductors. The comparison leads us to suggest the importance
of dopant size mismatch as a cause of dopant clustering, electronic
inhomogeneity, and strong vortex pinning.
