Have an arena (either single or team) that fight a boss (I guess the boss can either be random or chosen depending on what the player unlocked) one on one.
Players can put bets down on who'll win and spectate the match.
Team competition wise, you can have multiple teams to see who can beat the arena.
I like the ideas of spectating. I think guild v guild in battlegrounds should allow players to spectate and bet money. This could create a really great way for guilds to make money and publicize their skills.
Argent tournament - already done, must be a wow clone idea....
Seriously though, a gladiator style events that had multiple competitions would be awesome! The GDC video showed some time trial dungeon encounters. I think they could do lots of interesting things with that. Vanarch could put up prize money and have a sponsored tournament.....
I doubt that a lot of people would watch other people do PvE in-game. They can just watch YouTube videos if they want to watch someone else play. PvP tournaments are a different story.