Jenny Wagner gives us the observational case for and against the Cosmological Principle, based on a paper she and 22 co-authors wrote summarising this case.
She starts by clearly defining what the Cosmological Principle is and then talks us through the observations that she and her coauthors find to be the most compelling evidence against the assumptions of full statistical isotropy and homogeneity. In each case she gives us the story either “side” would need to tell to reconcile the observation (the standard, FLRW side and the inhomogeneous cosmology side).
Cosmology Talks 