I am planning to setup different Kubernetes clusters in different data centers which are interconnected.
Is it OK/a good idea to reuse the cluster IP range across the different Kubernetes clusters? That's, different clusters use the same IP range as the cluster IP range to save the IPv4 address space. If not, what will be the potential risks for the reusing?
You can not "share" cluster IP range. Even if you define the same one, each kube cluster will manage it on its own, hence it will be possible to have same clusterIP for different services in different clusters. Kube-proxy will also talk only to the API of the cluster so you will not be able to connect to svc from another cluster by means of "internal" communication.
Although not exactly in this scope, you may find Kubernetes Federation of interest to you.