Are you seeing water staining on the ceiling beneath the shower? If not, then I suspect the shower pan is intact and the building materials under the shower are ok. That said, the standing water saturating the pan may result in time popping loose. I don't think you need to worry about black mold at this point.

A lot of showers are built without moisture barriers, although I think it's cutting a corner. I ripped out a 3 year old shower in my previous house that didn't have a moisture barrier and there wasn't a lick of mold (ripped it out to change the tile, not because of mold or moisture problems). I am going to guess that the wall tile is set in cement board, which is water resistant, which is why builders don't use a barrier, but not waterproof. As for the floor, using tar to waterproof the pan is routine, you should be ok. Again, I think the bigger concern is whether tile will pop loose on the floor.

I agree but disagree. What do you mean by "water to pool", does the shower drain quickly? Do you seebird bath's, or does the tile hold up water from getting to the drain? By tar, I assume you mean hot mop, are you in California by chance? I believe waterproofing the walls is essential, cement board is in my opinion not very water resistant.

The water drains fine from most parts, but there are areas that puddle because the floor is wavy, like when you see puddles on a sidewalk because the cement isn't level.

I'm in NC....I have no idea if it is hot mop, but if that is some kind of black tar then yes lol

"puddles on a sidewalk"

Or birdbaths, not pitched properly. Didn't know east coast still hot mopped, combine all this with no waterproofing on the walls and you possibly have a mess on your hands. Do you any pics under construction?

No, not of the shower specifically. I do know there was no plastic involved. I believe the pan is cement board with the tar over it.