I like the idea of being able to access the mission panel from your omni-tool. (with a name like "omni", it should be able to handle something like that.)
But I actually liked the idea of the war table missions taking place "real-time".
I liked how I could start a mission that would take 6 hours at around 9 PM, then go to bed.
I wake up in the morning, and whenever I get around to booting up the game, *VOILA!*, I have a reward ready and waiting to be collected.
Of course, it helped that I always saved right outside the war room, so every time it would just be a simple click and I can grab the stuff, so I see why it would bother people who saved in the middle of the Hissing Wastes and then have to travel across loading screens just to get +89 gold.
(I also found it reduced load-times if I transitioned to a new zone by myself, i.e. without a party, and then select companions using the little horn at camps when I arrive.)
Another thing that I feel would add to the missions is being able to start them from different locations.
Such as a diplomatic mission.
Some group wants to talk about a territory claim, so you can have the talks at (A) a military base, (
your headquarters, or © a colony.
If you complete the mission at the military base, they see your might and revoke their claim. But they might build up and attack later.
If you complete the mission at your HQ, you can make an exchange of 200 eezo to allow your ship(s) free passage. But they might ask for more later.
If you complete the mission at a colony, you can befriend them and gain some colonists/population for that colony. But that might create problems for your colony later.
I know that sounds a bit like Cullen, Leliana, and Josephine, and it does, but rather than have it all just be flavor text (to be clear, there's nothing wrong with that), you could have a physical location for the mission to occur.
It'd be a great way to implement Paragon/Renegade decisions, see the results of previous decisions (*We appreciate your peaceful resolution of the Selenova Incident*, *We heard how you... handled the Selenova Incident*), and you could have a hand in creating new missions (if it goes well) hubs/bases/alliances (if it goes really well), new battlegrounds (if it goes badly), or outright genocide (if it goes really badly).
In summary, the War Table is a great idea, it just needs some polish.
And there needs to be more than one "table", as it were.