Ambiguous mission objectives and scenarios
Overlapping Objectives: You may only complete one mission per turn, even if you have achieved the objectives on multiple mission cards, and only on the turn which you achieved the objective. On page 17, under Completing a Mission (emphasis mine).



  Completing a Mission 
  
  You may claim a completed mission once you have achieved what it says on the card. But you cannot claim more than one mission on a turn.


Update: You may only complete missions if you achieve the objectives that turn. There are 3 examples of when mission cards can be claimed. 

1) Play at the Start of your Turn: before Reinforcements.

2) Play after you gain Reinforcements: show when you receive reinforcements (either during the reinforcement step, or at any time you have 5+ cards in hand)

3) Play at the end of your Turn: after drawing a territory card (if applicable).

I imagine it would be a nightmare if you would be required to remember all a players action since the beginning of the game as proof that you did/didn't complete some mission objective. The rulebook doesn't state clearly that you have to complete the mission objectives on the turn that you claim the card, but years of Risk history would indicate that this is the correct interpretation. This would further be clearer if the "Control X continents/territory cards" all had (play at the Start of your Turn) since you cannot change the number of continents/territories you control until your combat step, the "Conquer X continents/territory cards" all had (play at the End of your Turn) after your combat step, and all "Gain X+ reinforcements" cards with (play after you gain reinforcements) since that is when you gain reinforcements. The alternative, of counting all your actions since the beginning of the game, would make it easy to complete many of the missions +3 troops per turn allows you claim 18+ troops on turn 6, conquer X+ territories cards would require a pen &amp; paper to keep track of, etc.

As for the differentiating factor for the Mission Cards, they are sorted by the type printed on their card backs (page 17), General, Major, Colonel, Captain. I would surmise that they there are differing levels of difficult in completing these goals, but the rulebook doesn't say.




Sparse Reinforcements: You may only use an opponents territory cards to gain further reinforcements during a turn, if you have 5+ territory cards in hand. The rules specifically state the steps in your turn on page 7. You will note that Combat happens after Reinforcements. You can only gain a players territory cards from eliminating them during Combat, so it is too late in your current turn to purchase reinforcements during your normal Step 1. The only exception to this is on page 12, under Eliminating Another Player: that says, "if your new hand of Territory cards is now 5 or more, you must stop immediately turn in a set in for bonus reinforcements. Since you may play the mission card after gaining reinforcements, you can play it during this bonus reinforcement step. You probably can also count any reinforcements you have gained since the start of this turn (during Step 1), and any troops you gain during this bonus step towards fulfilling this requirement.



  Step 1: Receive and Place Reinforcements (always)
  
  Step 2: Combat (if you like)
  
  Step 3: Fortify your Position (if you like)
  
  Step 4: Collect a Territory Card (if you have conquered at least one territory)





Eliminated Players: Yes, any number of territories is twice as many as zero.


I agree with this statement. An eliminated player clearly has zero territories, and zero times any number is zero (2 x 0 = 0). Therefore, any number of territories (including 0) would be having twice as many territories as any 1 enemy.


0 - 0 or more
1 - 2 or more
2 - 4 or more
...