This question links to a post from the Temple Institute that mentions that a red heifer was born in Israel in 2002 and that a couple of rabbis had traveled to check the cow and verified that it was indeed kosher to serve as a parah aduma. What properties were the rabbis looking for in their verification, and how rigorous is the vetting process?
Mishnah Parah 2:5
היו בה שתי שערות לבנות או שחורות, בתוך גומה אחת, או בתוך שתי כוסות והן מוכיחות זו על זו--פסולה.
If it has 2 white or black hairs within one "depression," or within two "cups" in such a way that they clearly go together, it is invalid.
The Mishna goes on to discuss other details, such as if the roots are red.
Among other details, this would be a primary criterion to check, as the red hair is the defining feature of the red heifer.