Background: There is an urgent need to better understand the mechanisms underlying acute and long-term neurological symptoms after COVID-19. Neuropathological studies can contribute to a better understanding of some of these mechanisms. Methods: We conducted a detailed postmortem neuropathological analysis of 32 patients who died due to COVID-19 during 2020 and 2021 in Austria. Results: All cases showed diffuse white matter damage with a diffuse microglial activation of a variable severity, including one case of hemorrhagic leukoencephalopathy. Some cases revealed mild inflammatory changes, including olfactory neuritis (25%), nodular brainstem encephalitis (31%), and cranial nerve neuritis (6%), which were similar to those observed in non-COVID-19 severely ill patients. One previously immunosuppressed patient developed acute herpes simplex encephalitis. Acute vascular pathologies (acute infarcts 22%, vascular thrombosis 12%, diffuse hypoxic–ischemic brain damage 40%) and pre-existing small vessel diseases (34%) were frequent findings. Moreover, silent neurodegenerative pathologies in elderly persons were common (AD neuropathologic changes 32%, age-related neuronal and glial tau pathologies 22%, Lewy bodies 9%, argyrophilic grain disease 12.5%, TDP43 pathology 6%). Conclusions: Our results support some previous neuropathological findings of apparently multifactorial and most likely indirect brain damage in the context of SARS-CoV-2 infection rather than virus-specific damage, and they are in line with the recent experimental data on SARS-CoV-2-related diffuse white matter damage, microglial activation, and cytokine release.