It wouldn't surprise me if there wasn't a bunch of mold and rot behind the walls there. The surround has gaps, and someone attempted a really poor application of caulk. My guess is that they also don't have the elbow (an dog-ear el) in the wall anchored so that the handles and spout could move in and out, making a decent looking seal tough to impossible.
Being a rental, I don't think I'd want to touch it. Asthetically, it's really poor, and functionally, may not be good, either.
There are spouts you can buy that would go flush to the surround but you'd have to clean off the pipe (can't have paint or caulk on it). The only way to fix the handles or showerhead would be to replace them.
It's unlikely that the valves are anti-scald, and it looks like they were replaced after that requirement came into effect. Now, there are probably still millions of showers out there without the anti-scald feature, but technically, it was probably not done with a permit or an inspection, was done after that was a requirement, and thus, is illegal. It only becomes potentially unsafe if there's issues with the plumbing supply lines and pressure (say, flushing the toilet drops the cold water pressure a lot and the shower becomes quite hot while the toilet refills). This isn't a certainty, but happens, thus the requirement to protect you from the potential effects.