I study aerodynamics, and haven't heard of problems from scaling down the models.
The main problem with supersonic wind tunnels is ensuring there's no interference from shock waves bouncing off the sides of the tunnel, which is why the X-plane program used actual airplanes. So wind tunnels are rated to a certain Mach, and above that, like for hypersonic, actual airplanes are still used.
FYI: I believe the DC-3 was the first passenger airplane designed with a wind tunnel, and as a result was efficient enough to be the first twin-engine commercial passenger airplane to fly over the Rockies with a safety margin to fly single-engine, and adequate to be the first proposed Shuttle wing design.
The main problem with supersonic wind tunnels is ensuring there's no interference from shock waves bouncing off the sides of the tunnel, which is why the X-plane program used actual airplanes. So wind tunnels are rated to a certain Mach, and above that, like for hypersonic, actual airplanes are still used.
FYI: I believe the DC-3 was the first passenger airplane designed with a wind tunnel, and as a result was efficient enough to be the first twin-engine commercial passenger airplane to fly over the Rockies with a safety margin to fly single-engine, and adequate to be the first proposed Shuttle wing design.