QuakeWorld, CPMA and Reflex[1] all have a very interesting feature : Multiview. This allows you to watch the viewpoints of numerous players at once. QW/QW/CPMA/CPMA
I believe this feature would be fairly nice if setup properly when it comes to spectating and learning from your play and also for coaches who are spectating. I believe custom HUDs for each multiview window would be a nice feature, preferably being able to customize location and size of the multiview (this is possible in CPMA), along with other possible things such as static camera multiview for areas on the map and other various ideas. There's a large amount that could be done with this idea in practice
When it comes to spectating, I believe a Quakecon 2015 CTF hud combined with the CS weapon showing and occasional stats would likely be the best. Reducing potential disorientation during 0G locations would also be a nice thing to think about during spectating.
Generally, spectating class-based objective games like Dirty Bomb/Enemy Territory can be a lot harder than games like CS as the state of the game is not as well defined at any moment and due to the incredibly fast movement and somewhat low TTK. Take this in consideration and attempt to make the spectating experience more clearly define and show off the current state of the game, and make sure it can show off the moments that would be interesting to top players in a manner that can also interest those who have never touched the game before.
[1]I have not played Reflex for a long time, when I did play it the code existed but there was not UI so it was not enabled.