I've noticed that quite often DOff missions will appear to be ready to begin, as if you have all the DOffs you require, even though you do not.
Example: Shipboard Security Training Exercises requires a Security (division) officer, an Assault Squad officer, an Armory officer and two Security (specific) officers. On the DOff UI it appears to be available, but when I go to assign my officers I find I am short one Security (specific) officer. So, I actually cannot start the mission.
This always happens when more than one of any single type of officer is required for a mission. Missions with multiple slots for such an officer cannot tell the difference between many and one officer in your reserve.