Testing is a job by itself requiring, for a flight sim, knowledge in software architecture, real time processing, physics, AGILE (…) test strategy and test planning because it is extremely complex or complicated to test. The difference between Complex and Complicated can be found here in the Cynefin framework.
I wrote an article about what it takes to test a Full Flight Simulator and you can find in the article the suggested skills for a tester and what an extremely refined simulator can do in general.
For aircraft handling a base needs to be established: We call that a QTG. A QTG is a set of objective and subjective tests coming from EASA or FAA. This link is the list of tests that would catch many deviation in aerodynamics, atmosphere modeling, ground model, aircraft model. It is quite large doc but if you are curious about how we test real sims it is worth to have a peek at it. We can complain that some aircraft systems are not perfect, but let’s be honest, they are hard to reverse engineer due the sheer complexity of modern aircraft, and not to mention the exposure on patent infringement that could pop out. Looking for a skilled tester?