The metal wall to the east of the pedestal on which the red skull key sits is misaligned. Open this wall to find a soul sphere (sector 298).
In the room with the metal pillars before the blue skull key, press on the second pillar from the east in the southern row. It will lower to reveal a soul sphere.
If the player grabs the chaingun at the beginning of the level (or at least enters the inset it rests in), he triggers first (Linedef 1754; Action: 110 - W1 Door Close (fast), Tag 2) sector 301 to block the original switch (Linedef 1127; Action: 114 - SR Door Open Wait Close (fast), Tag 15) that opens the way to the exit room, then (Linedef 1771; Action: 109 - W1 Door Open Stay (fast), Tag 7) sector 302 to reveal a new switch (Linedef 1769; Action: 114 - SR Door Open Wait Close (fast), Tag 15) with the same function. (It is possible to close the original switch and leave the new switch blocked by slightly entering the chaingun's inset on its eastern half.)
The new switch is much closer to door that it opens for a short time, making the process of reaching that room much easier. In fact, it is possible to reach the exit room without grabbing the chaingun, but it is so difficult, that this has to be considered a single-player bug.
In multiplayer, blue torches are blocking the chaingun alcove, so the original switch has to be used.
There is deathmatch player spawn (Thing 13) in the alcove where the BFG9000 rests (sector 99). Leaving or entering (through the passable grid) this alcove triggers (Linedef 560; Action: 2 - W1 Door Open Stay, Tag 17) two walls to lower:
Sector 214 (at the regular map start location right north of the four backpacks) that reveals the megasphere and sector 210 that opens a teleporter alcove nearby the plasma gun. This teleporter's destination is that BFG9000 alcove.
Thus, the megasphere and the BFG can only be obtained in deathmatch, resulting in only 75% of the items can be picked up. (Unless using the idclipcheat or abnormally jumping up 200 map units into that alcove. Entering player-jump-power 19 in Doomsday's console allows the player to jump at that height. Default is player-jump-power 9.)
Areas / screenshots
Routes and tricks
The switch that lowers the red key pedestal can be triggered before it is raised. Stand below the center of the eastern skylight in the hall before the red key room, and flip the switch from the east.