Spoilers; This Movie Is Full of Plot Holes
If Amy Adams can simply "remember" a phrase in Mandarin, and can "remember" a phone number that she has never seen before, then why couldn't the aliens "remember" how to write in English (or any human language) and simply write "we come in peace" from the very beginning?
It seems that aliens smart enough to travel through space without emitting waste and with the superpower of clairvoyance should be able to figure out a simple plan to use these powers to communicate with humans in a non-vague way like "use the weapon".
And if they can see the future why did the aliens not know there was a bomb on their spaceship and push Amy Adams and Jeremy Renner out of the spaceship earlier so they could have time to run for cover?
Also, why did they arrive in 12 different locations and make it a puzzle? Why couldn't they just arrive in one or two locations? And if they knew that the Chinese were super crazy and violent why not just land somewhere else?
When you consider that the aliens could see the future it makes all the conflict in the movie seem unnecessary. These are beings that plan thousands of years in advance but they can't come up with a more efficient plan for making contact with humanity?