Example 1: In the Overseer's hidden chamber, one finds bras strewn about the floor, soft music playing, empty liquor bottles, and a narcissistic paining of himself on display (the same one you see Sokolov painting in the prologue). An audio log further explains his character, explaining his frequent visits to "inspect" the Golden Cat (which you will visit shortly thereafter - hooray foreshadowing). This area gives the player some underlying notes about the Overseer and how corrupt he is; besides attempting to poison Curnow and benefiting from the coup, he partakes heartily in the vices the church he leads preaches against. (Also perhaps a not-too-subtle jab at real-life organized religions.) It fills out the target's immediate history and may influence your emotions as the dispenser of his fate. While assassination seems a fair price for his crimes, branding him as a traitor and sinner is bitter and just. According to his own church's tenants, he is surely a sinner. Going non-lethal also results in a terrifying surprise much later in the Flooded District, where you can find him, now a plague-riddled Weeper in the depths of an abandoned, rotting building. A note lies on the ground; his final coherent thoughts are a seething curse against Corvo. Also worth noting is the painting of the Overseer in his chamber is missing the liquor prop if you took it during the prologue.
Example 2: The whale oil seeping wastefully from the Flooded District. Here is this fuel the city is so dependent on - and seems to be running out of - just laying around, spilling everywhere, leaking into the river. Seeing as the reason the Flooded District became flooded in the first place was due to simple laziness, it's not surprising that it is also due to laziness that these caches of oil are not being recovered. When viewed as part of the big picture, a picture is formed of how wasteful this city is, and how the powerful seem to be avoiding the problem, holed up in their towers and mansions.
Example 3: Tying into the idea of excess and decline, the Boyles' party is striking. They are essentially ignoring the outside world and the poor surrounding them. The Boyles' mansion is among the most beautiful and extravagant spectacles in the game, but is surrounded by poverty, the plague, death, and Weepers. They're either oblivious or purposefully blocking it out of their minds by putting on a showy party. The city watch are more concerned with keeping unwanted people out of the party than they are with taking care of the streets. The fact that your first encounter with Tallboys is outside the mansion gates is telling. The Boyles' guests chat about trivial things, encourage you when you steal property, and come off as lousy, entitled people. It's kind of a depressing mission despite the exquisite setting.
Example 4: In mission 3, there is a courtesan in the Golden Cat that is alone, smoking a cigarette in her dingy quarters, hidden away from clients and the rest of the otherwise beautiful premises. If you look closely, you can see that she has been crying, as her eye shadow is dripping down her eyes. Examine the room, and you see a letter from her family, who is looking desperately for her. It seems they are close to finding her, yet very far due to stonewalling from the Golden Cat's staff. This pairs well with what the Heart has to say about the mission. Pretty sad stuff.
Example 5: The wanted posters throughout the game often pair the player's poster next to Daud's. This could be seen as a nod to the fact that you are both wanted men with similar skill sets. Despite being at odds, he can be perceived as Corvo's equal and rival. Seeing as he is the man that killed the Empress/your lover/the mother of your child, being next to each other on the wanted board is kind of interesting. He also is the only enemy in the game that is immune to bend time, should you choose to outright duel him. If you watch and wait, you will hear that he expresses remorse for killing the Empress and wishes to strike at the Lord Regent, which may influence your decision to take him down or spare him.
There are other little details and visual clues that, while maybe not especially meaningful, are nice touches and add value to the environments: the detailed ironwork on the Golden Cat's exterior, the detail in the rugs being slightly scrunched and lifted off the ground in the Overseer's building, the posters plastered over the windows in Dr. Galvani's laboratory (covering up his work from prying eyes). I noticed the guards wear air-filter masks earlier in the game if you go down the High Chaos path.
