I can only speak from experience, but, IMO, the show overdid the amount of grime in hospitals, and misunderstood some sources of grime that were endemic to Soviet Union.

Probably, the chipped tiles were the most endemic. The reasons for this were many: tiles were in constant demand, so they were routinely stolen; Soviets didn't really manufacture ready-made tile concrete, tile grout, tile setters and the like; as a result, the tile jobs were either shoddy - or very time consuming. However, tiles were extremely durable and easy to clean, so Soviet architecture used it a lot, so you could run into bad tiles pretty much everywhere.

Soviet buildings would typically either be concrete, with walls painted directly over concrete - or brick, with stucco over brick, and the said stucco being panted over. However, even small drips would routinely destroy stucco, and as Soviet water proofing was quite poor, big "gaps" in paint caused by the destroyed stucco were also quite routine, and very bad if the building was abandoned, as in many of Chernobyl chronicles.

This being said, stucco was actually relatively easy to repair, and thick oil based paint would be applied liberally. As a result, a lot of scenes in the series look like run-down building, but not as the high profile buildings in regular use.

Finally, private apartments. Getting you apartment into a decent shape was a major project for many families, and a point of pride and joy; as a rule, people with more money would try to put their apartments into better shape, which included wallpapers over stucco or concrete, decent stolen tile in the kitchen, better furniture and the like. In this regard, Legasov's home is quite inaccurate.