When you exit the keep, take a right turn and find a balcony with a glowing object ahead on your left. Jump up (use the nearby roof) for a Combat Staff and a Full Health Potion.
Near the map exit (where Leanna is) you can find a ladder. Climb through a window to an attic for some potions. From here, you can exit from the windows on the opposite side and reach another balcony with an apple. This doesn't count as a secret area, though.
On the upper floor of an unlocked house, turning a lamp on the wall will unlock a secret area with a pair of Cutting Kriss.
When you enter the keep basement, take the door on your right and find a pile of barrels in a corner. If you remove them, you'll find a Ring of the Weaponmaster.
From here, follow the corridor to a depressed area with clutter and two guards. In the lower area, there is a rock on the ground near the wall that you can push to open a secret area with some potions.
When you find Menelag's throne room, check the study at the foot of the throne room stairs. Use the Strange Candelabra to unlock the fireplace for a Ring of Arcane Brilliance.
In the library, pull a lever on the wall to bring down a rope. Climb up and drop down into a walled-off area for a secret.
Right after the library (before the area transition and ladder to the roof) there's a dark wooden door about cat-height in a stone wall. Open it and cross some rafters for another secret.
When you wake up, jump in the water and swim to find a secret area with a Lightning Shield and some potions.
After escaping the worm, you will come to a high room with Facehuggers. Use the Rope Bow to climb into a hole opposite your entrance. You will go through a spider room and into a secret area.
From the ledge of the previous secret area, drop down on the next ledge for another secret area and a Bow of Fiery Rage.
After the Facehugger room, you will find a high "waterhole" where you must raise the water level to proceed. There is a hole in the wall with a rafter above it that you can reach from the bottom with your Rope Bow for a Master Thief's Outfit. Alternatively you can just grab it when the water is rising.
On top of the waterhole, there's a narrow ledge with a Magic Mushroom.
On top of the waterhole, there's another hole in the wall with a rafter. You can either use the Rope Bow, or take the waterhole exit corridor, turn left and climb (there's another Magic Mushroom at the spot you must climb) for another secret area with potions and scrolls.
After the waterhole, some mines, and two chain cart rides, you will end up at the orc city. Get out of the cart and start left, staying on the top level. Follow the ledge all the way to a small hut with a Magic Mushroom behind it and a rafter above. Use the Rope Bow for a Shadowsteel Armor.