The main critiques of Customary International Law are that the two requirements of state practice and opinion juris are too simplistic. There is not enough guidance from scholarship vis what is meant by these two requirements. Customary IL is in the ‘eye of the beholder’. There is no reason for the rule of custom or lack thereof. The science of customary law is lacking. Guidance from ICJ is vague. Opinion juris is also vague.
A secondary criticism is that customary law doesn’t mean anything because such a disconnect between customary law and reality. There are many human rights norms for example that are part of customary IL, but they are continually breached. What is the weight of customary norms? Presumably not much because the impact on activities on the ground is minimal.