Kubernetes log processing poses several challenges, including collecting logs from multiple pods on each node, dealing with noisy environments and single errors causing more issues, handling namespace logging preferences without affecting security, and ensuring critical logs are collected even when pods are deleted and recreated quickly. To overcome these challenges, developers can use managed services that handle logging setup, configure CRDs for custom resource definitions, employ log agents to scan new folders or log patterns at regular intervals, and handle layered logging by understanding the characteristics and priorities of different logs. By using a managed service like CAST AI, developers can gain end-to-end visibility, troubleshoot issues efficiently, and have the freedom to choose tools that suit their needs without being locked into a specific cloud provider.