ROME — The grass in some public parks sways knee high. Disgruntled subway workers have slowed service to a crawl. Fire has rendered the city’s largest airport crammed and chaotic. The arrests of public officials pile up, revealing mob infiltration of the city government.

It all adds up to what Romans call “degrado” — the degradation of services, buildings and their standard of living — and the general sense that their ancient city, even more than usual, is falling apart.

Not all those troubles are necessarily the fault of Mayor Ignazio Marino, a former surgeon whose own integrity remains unblemished. But, strangely enough, in Rome, his decency is not necessarily seen as part of the solution, either.

Born in Genoa and trained in the United States, Mr. Marino took office in 2013 as the unlikely leader of a city famed for its political intrigues. His outsider résumé initially appealed to Romans hoping for an honest broker with Anglo-Saxon credentials who could clean up their city.