In Black Plague: in the machine room, you have to open a door with a metal bar. There are two metal bars around: one behind some barrels soon after you enter the machine room and one in the corner on your right when you are facing the locked door.
Now if you are dumb enough to throw both of them into the pit, a bar will magically appear in the door. I tried this because I wanted to see if I could get the game in an unsolvable state, but the devs thought of this.
In Requiem: in the sewers there are two globes. One at the bottom you simply have to dive for, another one much higher up. For the high one, you're supposed to use the dynamic platform, but it's not the only way. Make sure that before flooding the sewers you get at least three crates to the big circular area (you won't be able to dive for them if they are too far away). Now with the sewers flooded and three crates, you can carefully build a tower of crates on the pipes in the middle of the water, and jump to the path. It's not much harder or easier than using the dynamic platform, just different.