I think it would be fantastic to have a screenshot mode built into the player. It would be fantastic to capture those awesome moments. Every screenshot of the streamers stream should get saved onto their profile in a screenshot section. They can then decide which screenshots to keep or delete.
+1 for API capture
Allowing us to get the current frame of a stream (maybe only your own with auth) via API would be awesome too!
Yeah I was referring to the viewers doing it. Maybe I should have made it clearer :)
How about also allowing your viewers to hit the button then you can review it after? Cause, while your streaming, it may be difficult to get a good screenshot. :P