Sometimes it IS necessary to cut right through a floor joist to get a toilet in just the right spot. This frequently happens in remodeled older homes. The problem here is that it was not re-supported afterwards with the proper floor framing (using headers and trimmers). Because of this, the toilet in the bathroom above is very loose - and yes, it was already leaking!
If your shower looks anything like what’s pictured below, you might have a problem! What you’re seeing is a crack in the shower floor tile where someone used caulk as a repair. The only thing that may possibly be keeping water from actively leaking through to the room below is the shower floor pan below the tile. If I was in the room below, I would constantly be looking up at the ceiling – that shower pan won’t last long! The only remedy for this condition is to replace the shower floor tile and install a new shower floor pan.