Maybe it's odd, but I quite like the mission board in Warlords. It's quite a simple minigame, but it has the same polish shared by everything Blizzard does. Plus the integration with the rest of the game makes it more rewarding.
The only thing I don't really like is the 10-hour missions. In my opinion, scheduling missions would be much cleaner if the longest missions were 7, or even 6, hours.
The thing is that for most people, the day is divided roughly into three 8-hour segments. Eight hours of work, eight of leisure time, then eight of sleep. This translates nicely into queuing missions at the beginning of each period - directly before and after work, and before bedtime.
So if a mission is longer than 8 hours, there is already a problem, in that it will not finish during one of those periods. So at the beginning of the next period, either you wait, or you don't have access to all your followers. This is annoying. Plus it tends to compound itself, as when the 10-hour mission is done your followers will be behind schedule on their next one.
However, even then the schedule is pretty easy to break. If you stay late at work, or have a commute, then you won't have time to complete a full 8-hour mission before bed. So I think it's best if some tolerance is built into the system. Otherwise you're pushed into playing at odd hours.
In general, if you're going to include real-time barriers to progression, I think it's better to make them on the lenient side. Having to adjust your schedule just to play the game is rarely a good idea.