Surely enough I put many "secret passages", because secret passages are cool. Yet aside from being cool and providing a questionable escape benefit, what is their purpose?
Let's take a moment to think about all the cool things that could be in a dungeon that have a purpose aside from being secret and cool.
Deep dungeon sections need to have direct vents to the outside. Otherwise you're just breathing the rebreathed air of all the creatures between here and the dungeon entrance. And that's allowing for good sanitary practices which are seldom the norm in dungeons. Specially after they've been abandoned and take over by orcs, ogres, goblins, bugbears and the like.
So somewhere, somehow, there has to be a way to connect that room you're in to the outside world. Maybe the tunnel's roof (which you can't see) has vent ducts to the surface.
What about kitchens and cooking areas? How did they original inhabitants feed themselves? Did the guards go up five dungeon levels to eat or did they cook things locally?
There has to be a way to drain water from the dungeon. Deep underground water may flow out the walls and there has to be a way to get rid of it. Creatures will also produce liquid waste and will want to get rid of it one way or another. Specially the more intelligent and advanced they are. What mechanisms does your dungeon provide for that? Are there drainage tunnels below the main tunnels? Such a drainage system may connect rooms in an unexpected and very beneficial way.
Water, drinkable water, needs to be provided to the inner parts of the dungeon. Either to drink or to clean up. Where are the living quarter areas? Whoever built the dungeon did it to be manned by some type of creature, human or otherwise, and although they may be inhumane to prisoners they certainly had to have an expectation when it comes to standards of living for the guards and higher ranking staff. Right? How do you provide that if you don't have a nice and reliable source of water. It would be really really really bad to wake up thirsty at night or with a terrible hangover only to realize you have to craw up three dungeon levels for a mug of water.
It can get cold in a dungeon (it can also get hot). Some parts may actually be very cold and damp while others warm due to geothermal activity. Does the dungeon have Roman style floors to heat the room and turn the wizard's study into a more comfortable area to spend long winter days in?
What about baths? I'm sure the great overlord of the dungeon must have enjoyed a warm bath in a pool inside the dungeon. If I spent a fortune making my dungeon I'd at least add the basic comforts of life.
As you can see from the images the heating system can be considerably more complex and interesting to explore than the dungeon itself. Now that the dungeon has been abandoned, what lives in the pool? Has it made its lair out of the boiler area? What dwells in the crawlspace below the floor? Is the floor sturdy enough to hold a fully armored party or will some tiles collapse dropping party members into the hands of whatever lives down there now.
So you think they walked the manticore into the dungeon like this? And you actually think it went in on its own free will? Lead by a chain and all?
I'm quite confident it was more like this.
That spells a great deal of staff and service tunnels to bring those cages in. Because I'm quite certain that thing isn't going to take the right turn down that 10' tunnel very well.
So the dungeon will surely have big service tunnels leading to the surface through which creatures can be brought into the wizard's rooms, labs and even a coliseum. It's very probable that the passages being explored by the party members now are but a fraction of the whole. Below these narrow passages is a wide set of tunnels providing water, air, heat, and passage in and out for all that is required by the dungeon owner.
Now what do these tunnels look like? Are they small and only exploitable after using a spell to make a party member small? Are they big enough to craw through? Can someone kneel or walk around half standing up? Will a small character class like a dwarf or halfling fit comfortably? Or are they huge, capable of letting a wagon through it? Who built this and to what specifications?
So, try connecting all your dungeon levels and rooms with all that is required to provide a sustainable living environment and see it come to life with a complexity that will amaze even the most experienced dungeon crawler.