The chat log itself needs a report feature tied to the chatting menu feature in order to capture exactly who said what and when.
The chat log also needs a way to block messages from individual players. Basically the 2 features that are right there on the PC's chat mean that console is missing. 

Reporting and Blocking on PSN doesn't work. Blocking a user on PSN doesn't block in-game messages. The report feature on PSN is only for content on outside of games. PSN even says that reports for in-game actions have to handled by the game the issues happened in.