Well, Constantinople, Rome... they enjoyed a sewer system and wastewater collection which engineers are still copied today. And they also had a very effective cleaning of roadways. I can not imagine the centurions dodging horse poop or slipping on them. The Roman military dignity would not allow such a risk. The filth and dirt appeared centuries later with the arrival of the dark ages of medievalism and the deculturalization of the people. ›››
The Romans did have street cleaners and held property owners responsible for the street in front of their houses. Street cleaning was one of the most visible public functions of the aediles
. But there was still more mud and filth than could be cleaned up, and more chaos than could be well controlled; Juvenal wrote of mud up to his shins, tiles falling off roofs, pots flung out of windows, impudent drunks, traffic jams, and so forth. Not even Rome was quite so shining as one may imagine.
Medieval cities also had sanitation; London had street cleaners, an aqueduct, toilets and sewers, dumping laws, laws against transporting offal through the streets or pitching household waste out one's window (Gardyloo!
). These were variably enforced and not always carried out; for instance, street cleaners did not work in the rain (and it rained a lot in London then, too). It was not "dark ages" or "deculturalization" that led to filthy cities, but the overwhelming of services by migration to the cities.
This does not take away from the Roman achievements. Roman architecture, materials science, civil engineering, and city planning were unsurpassed for many centuries, and they have never been discarded, rather built upon and made newer. But the cities of the Middle Ages were not mere degraded echoes of Rome or Byzantium.