IMHO, the greatest "danger" is that it runs too long and overheats the aquarium. The risk of this, is primarily that the Apex temp probe goes insane, and gives out a value that is 5 degrees too low or something.
So lets say your set-temp is 78. I would set the temp controller to turn off at 80. Then program the Apex to hold the temp at 78. Additionally, program it to turn OFF at something like 65. Then plug the heater into the temp controller, and the controller into the Apex.
Rationale:
1) If the temp is below 65, either you haven't been paying attention at all to your aquarium when the heater failed and the house turned to ice, or the Apex temp probe failed. (solution, $3 digital thermometer, just look at it daily).
2) If the Apex goes insane, and just turns the outlet on forever, the temp controller will shut itself off when it hits 80.
3) In normal operating circumstances, the apex turns it on at 77.8 or whatever, and turns off at 78.2 or whatever, and the controller is well within the range of 80, so it's "on", so everything is wonderful.
Once in awhile, when the heater is on, look at the temp on the controller, and check that it is within a sane range of both the apex, and the little digital one.
I would also use a When statement on the heater. Set some value like, 2 hours, or whatever you feel is safe for your heater size vs aquarium. This is like a circuit breaker. If the heater runs longer than this time, it will switch to OFF, and need to be MANUALLY reset to auto. This means if the Apex decides the temp probe is permanently stuck at say 75, and it needs to run the heater forever, it will shut off after 2 hours no matter what. You can also configure an alarm for this condition.
The only other thing I might do is add a second Apex temp probe as a sanity check against the first one. The most likely bad apex scenario is the temp probe becomes exposed to air, and reads room temperature rather than tank. So each probe should be in a different area of the tank, mounted in a different way.
Now you have like.. 4-5 forms of redundancy, and if you still cook your tank with this setup, I'm not convinced you either pay attention, or could have prevented it.
