Hi, I'm not an electrical specialist but I've worked on design of such things with folks who are. I have a few comments based on my experience in photofinishing.
First, you are using a proportional-style controller, but using it to turn on a relay. Now relays are essentially remote-control on/off switches, so they don't have things like half power, etc., they are either on or off. So I don't think a proportional control is the proper way to operate a relay - you need a controller that turns the relay on or off. A relay IS a good way to operate a large heater like your 1500 watt unit. However... I share mgb74's concern about too much temperature variation. I think, for tight temperature control of a relatively small water bath, you'd be better served by a control system that can vary power to the heating element. Now I don't know for sure, but I suspect that they may be costly in a size to handle your big heater.
A few words on controlling water temp: the system design, in general, is fairly critical. You want to have a circulation pattern that minimizes the temp variations - for example, if you have a "dead spot," the temperature there will tend towards ambient. Even given good circulation, placement of the sensor can be crucial. For example, if you need only a slight increase in temperature your system will turn on the (large) heater at full power - water right next to the heater will begin to heat right away. But if it takes, say 5 seconds for the warmed water to reach the temp sensor, you may have done enough heating to significantly overshoot your aim. It might seem like the solution to this is to put the sensor right next to the heater - the problem with this is that the sensor will see the heat right away, and might turn off the heater right away. So if you are starting with a cold tank, it might take a long time, with many on/off cycles, to warm up. My point is that there is more to a good design than meets the eye.
Regarding safety, I am by no means expert in this sort of thing. But I think a lot of this depends on the heating element itself, as well as having a good earth ground for it. Internally in your control box I don't see any fuses. So if you have an internal short circuit (even in the heating element), you are relying on the electrical supply system to blow a circuit breaker. I wouldn't want to count on this, especially since I don't have any idea of the amperage capacity of that circuit, and it may be more than your controller wiring can handle. So I would want a fuse built into the control box. And if it's a metal box, be sure the chassis is grounded (you would expect that the GFCI would sense any current leaks and break the circuit, but what if your controller is eventually moved to a non-GFCI circuit).
As a note on your diagram, the +/- notation is really for DC systems. You are (presumably) using AC, where the standard U.S. terminology for standard household current (~120 VAC) is to speak of a "hot" line and a "neutral" line, see here:
https://en.m.wikipedia.org/wiki/Electrical_wiring_in_North_America
Best wishes on the project. Hope this doesn't scare you off.