Options include looking for discoloration on surrounding areas and even putting a paper towel or Kleenex in suspect areas in order to detect a small leak that may not have been sufficient to create noticeable discoloration. Depending on the volume, you may be able to hear dripping in order to help trace the leak. And you may wish to reconsider whether the initial diagnosis was correct or whether the repair was sufficient.
Here are three causes that weren't obvious to us that you may wish to consider:
(1) Around the tub spigot: We had a situation in which we had a leak from a bathroom on the ceiling of the dining room beneath it. We re-caulked the tub and shower surround, did a small test, didn't see any water leaking, and thought we'd taken care of the problem. The next time someone showered the leak reappeared. We eventually figured out that the problem was around the spigot: Water from the shower was hitting the spigot, and because there was not a good seal around the spigot, water was running behind the spigot, down to the floor, and eventually into the dining room below.
(2) The actual copper supply line connections--if you're fortunate enough to have access to them without tearing out the wall: In another house, one with only one floor, we thought we had a leak in our shower pan, but during a remodeling discovered that the hot supply line had not been soldered correctly and water had been squirting out between the wall and eventually out through the brick in the adjoining exterior wall.
(3) Diversion due to insulation: We had another leak that we thought was due to a problem with the flashing between the roof and adjoining siding. After tearing up the roof and the ceiling of the room being damaged, we discovered that the problem a poorly-sealed nail in the roof itself. However, this location was several feet away from where water damage showed up. In this case, the insulation directly below the small leak was sufficient to keep the water from running straight down. Instead it wound around and into another room.
To answer the specific question, you should replace any sheetrock that has mold. A one-time leak for a day won't cause this -- significant mold arrives when an organic material stays wet for an extended period of time (weeks or more, usually) so you should make sure it's dry before it's repaired.
The bigger problem is what is being covered up. You need to know what was the cause of the leak and be convinced that it has been corrected properly. You need to check what you can see for any blackness (i.e. mold). If you find more than a couple dots, then there are moisture problems beyond this one major leak and the ceiling and walls need to be removed until the full extent of the problem is known and removed. Don't do this yourself! Contact a professional remediation company.
Same for the floor. A one-time thing, even this big, won't cause mold as long as it is fully cleaned up and allowed to dry out completely. This can be difficult if the water has gotten beneath the surface as it certainly will with carpet, hardwood, etc.; you may have to remove everything down to the subfloor, let it dry, and re-install.
The brown water is a concern. If it was waste water, then you may have a health hazard and you'll need an environmental assessment.
I understand that this is not property you own, which makes getting this done difficult. I suggest you do what investigation you can, consult with an unbiased professional, and talk politely with the landlord about your concerns. If you're not satisfied with the answer, you can take your concerns to the government (mold and waste water are health hazards) and find a new place to live.
Best Answer
If the floor is warm and you hear a hiss, it's not "slowly" leaking, it's spraying in a significant quantity. Prepare for a large utility bill, and go shut off your water supply. It takes a pretty significant leak to noticeably warm the floor, in my (unfortunate, and that was a BIG gas bill) experience.