I would like the training dojo to allow you to fight your friends teams while A.I. Controls their team(maybe even player controlled). I made a similar thread to this one before stating that we need more friend interaction in the game, and I think this would be perfect. Im sure you guys have your own ideas and opinions on what you want or think the dojo will be, so go ahead and share.
I expect trainers dojo to be the same sort of thing as the six trials. In other words, the super silver, omegamid and super youth fruit events will be made into dungeons that require tickets and can only be entered on a timed basis (probably once a week or 10 days or so). This will save the devs having to run the events as live events, just as they have done with the six trials.