I'd like to pose the concept of a replay feature for boss fights.

I envision the feature working like this:
Over the course of a trial each attempt could be individually saved to the server. These attempts would be numbered and at any time during a trial you could open the replay menu to see what attempt you're on. At the end of a trial before exiting you would have the option of selecting attempts to download to your local client. Once everyone leaves the trial all replays of the fights would be deleted from the server.

Viewer:
When viewing replays you could select any player and see a time-stamped log of abilities being used and who is being targetted when applicable. The camera could be set at any angle for screenshots and video clips.

With this feature Youtube guides could be a lot better and easier to make. Replays could be shared amongst the community for training, allowing players the ability to see detailed demonstrations of every job.