Refraction quality is lower in rendered image than in the viewport preview I was playing around with Glass BSDF shader to see what it look like and how it interacts with its environment. Bellow, you can see a test scene.

Preview

Final 
  The preview render on the sphere looks fine but when a final render was done the refraction of the checker-board was pixelated and distorted. The final render was done with 400 samples. Is that too little or am I missing something.
Is there a way to improve render quality of the refraction in the glass sphere?

File here :
The problem is that you are using flat shading on the mesh, as opposed to smooth shading that interpolates normals: https://docs.blender.org/manual/en/dev/modeling/meshes/editing/normals.html?highlight=smooth%20shading#shading

The reason why it looks ok in the viewport is that your subdivision surface modifier is set to 4 iterations for the viewport and 2 iterations for the final render. So the high subdivision in the viewport hides the flat shading.

Solution: Set viewport subdivisions equal or lower than final subdivisions, and enable smooth shading on the mesh (see above link).