Yep, I'd start looking for a better place from the sounds (and looks) of things. I seen/lived in situations that were worse ... but that was before I had kids. Glad we bought a house ... I sure don't miss the haggle with shifty owners. (I had 3 burst pipes in 1 1/2 yrs ... owners wouldn't compensate, insurance wanted 3 separate claims = 3 separate deductables = I get screwed in the end. Fortunately I had a great building manager who helped work out a deal).
The mold is a concern ... but still minor when it comes to legalities, the fact nothing is stated in your lease about fish tanks/aquariums, gives you the leg to stand on in court.
Let's say you had no fishes ... instead you grew prize quality fresh water plants, or salt-water coral. You wouldn't have anything someone could remotely call a "Pet". That's why its required for the lease to specifically state that an aquarium/fish tank is not allowed. Just like it has to specifically state about waterbeds. They fall into a category unto themselves.
You're biggest problem seems to be that the new owners and manager are pretty fresh (or else plain slum lords). And want to implement new rules and regs but don't understand the process in doing so.
Show them the pics of the closet, and see how they handle it. Don't try to hold it over there heads (save that for a later day), but approach it as a problem all its own. (no mention of your tanks ... unless they bring it up). This will give you an idea of whether or not its even worth the effort of trying to work with them.
Hope this helps.
These are the kinds of things you find in the fine print (as one member had mentioned), I learned a long time ago to read the fine print. But still the wording ... sometimes things still slip through.