In aerodynamics we have several "similarity" quantities such as the Reynolds Number which is a dimensionless coefficient that characterizes (in a nutshell) the ratio of inertial to viscous forces in a flow.

Much research has gone into the applicability of scale models to real world conditions and the validity of a model is contingent on maintaining similarity coefficients. So for example you want your model to be flying at the same Reynolds Number as your full size aircraft will. If you can achieve those conditions then you can expect good predictive results from your model.

In general you can learn a great deal about your aircraft from a model including handling and stability characteristics but you're limited by the tunnel and the test apparatus. Post stall behavior comes to mind as something I would imagine to be very difficult to investigate with a scale model in a tunnel.