The Kubernetes scheduler can lead to several problems such as degraded performance, high availability issues, and increased costs when scheduling pods without proper affinity or anti-affinity rules. Inter-pod affinity allows pods to be scheduled on the same topology as their matching pods, while inter-pod anti-affinity prevents them from being scheduled together. By using pod labels and defining affinity or anti-affinity rules, developers can solve problems such as network overload, high availability issues, and reduced costs by isolating pods on different nodes or in the same zone. Effective labeling strategies are crucial for creating effective affinity and anti-affinity rules to optimize Kubernetes cluster performance.