I'm using Frigidaire dehumidifier's to keep things in check for my current system. It's a small system and the dehumidifiers only kick on occasionally. Once I build out my basement sump and 180 gallon display tank, I plan to add an exhaust fan to the outside that will be controlled by a dehumidistat.
If you control the humidity, that should control the mold growth. If the opportunity presents itself, it wouldn't hurt to use products like moisture resistant plasterboard if you are doing any new construction around the fish room or the tank.
I'd be planning for floods and ways to mitigate the damage and drain the water away safely. For my current build, I'm planning to cover the bottom 2 to 4 inches of my tank stand with a shower membrane to create a water tight pan with a small drain at the low spot to take that water down to my basement. This should help to keep some of the water out of my dining room if the tank springs a leak or overflows. Even if you don't have a drain, just creating a water tight barrier at the bottom of the stand that would capture some overflow and hold it, could keep water off your floor. For my 6 foot by 2 foot stand, just water proofing the bottom 3 inches would create a bucket that can hold 22 gallons or so.
I have a floor drain in my unfinished basement and I'm going to make sure that any equipment that is part of my basement sump that can leak water will be placed so that the water will move to the floor drain.(the concrete slab is poured in a slope so that approximately half of my basement will flow to the floor drain while the other half is mainly flat and will not)
I'd also be worried about the electrical outlets near your tank and fishroom. Make them GFCI if you can. I also placed covers on mine that were designed to protect outside outlets from the weather. They are sort of like a small watertight box with a lid that lifts up to give you access to the outlet. They were easy to install and didn't require any modification to the wall. You can buy them at Home Depot for around $5 to $10. I sprang a leak in a hose in my sump once that was spraying water right towards the electrical outlet. That water tight cover on my outlet kept the socket dry and probably prevented something very bad from happening.