In the Learning the game section it says this about Missions:
If something you do in the game triggers two of
your mission cards at the same exact moment, you may only
play only one of them.
In the glossary it says this:
Only Play One Mission at a Time
If doing something in the game triggers
two of your mission cards at the same ex-
act moment, you must choose to play only
one of them (per turn).
Does this mean you can claim the other mission on your next turn? I would assume yes, but the wording is slightly ambiguous.