Common challenges encountered during a PCF deployment include issues with cloud infrastructure compatibility, complexities in managing cloud platform resources, difficulties in application development and deployment, ensuring seamless integration with different cloud platforms, managing performance metrics and application instances efficiently, addressing security concerns related to user accounts and personal information, handling continuous delivery and load balancing effectively, as well as optimizing application performance while dealing with cloud-native applications and containers. Additionally, challenges may arise in navigating the deployment of PCF across various cloud platforms like Google Cloud, Amazon Web Services (AWS), Microsoft Azure, and others, as well as ensuring smooth migration of applications to the cloud environment.