In the office building, when you enter the balcony around the center slime pit, turn right, look at the south wall and open a section marked by a standing health bonus. Inside a lava room you can find a soul sphere or medikits.
In the office building, when you get the yellow skull key on the northern lowered pillar in the slime pit, a new room becomes accessible in the western corridor. Find there a new corner marked by a picture on the wall and open it to get access to a room with a teleporter. The teleporter takes you to an L-shaped room with a ledge on western and southern sides. To get to the ledge sprint-jump from a top of the pyramid. Go through a fake wall on the eastern end of the ledge to get a BFG9000.
There is a green fort in the middle of the outside area. Before going out from the building, open a wall on the right from the door to find a blue armor.
The outside area is surrounded by the dark wall, of which one section is marked by blue torches. Lower this section, get an invulnerability sphere and you will find yourself on top of the nearby rock.
The following areas do not count towards your secrets, but are hidden and not required to complete the level:
In the office building, next to the room with the teleporter from Secret #2, there is a room with a square window seen from the eastern corridor. Inside you can find a megasphere. If you get the megasphere, you will be teleported to a room in the northern part of the office building, where you can find an invulnerability sphere (On Hurt Me Plenty or lower skill).