All manner of tests are done in fluid-dynamical modelling. Test suites are developed along with models. Simulations are done with a range of alternative models, or individual models with different conditions are applied, and the differences between the simulations are studied in detail. Models must rely on a fairly large set of parameterizations of processes that cannot be resolved directly, and tests are done to see which parameterizations make the most sense.
Models stem from the academic environment, not the business environment. This means that the models are open-source, so everyone can see what everyone else is doing. And 'everyone' is a pretty large set.
Note that there is no commercial element to any of this, which means there is no incentive to hide problems. It's the reverse: reputation is earned by finding problems, not by hiding them.
A large part of the challenge of climate modelling is the leveraging of increasing computer power to resolve progressively smaller scales of motion, and this uncovers the need to understand those scales in isolation. Modelling is often used at this level also.
None of this is to say that climate models are perfect. They obviously are not. But the system of academic science is very good at improving models and, importantly, exposing their limits. An indication of the latter is the pairing of uncertainties with predictions: a hallmark of this scientific community.