I don't like how this article implies that they aren't saving and storing all of your emails unless you are communicating with a surveillance target. In reality they are sucking up all data in transit and only looking at it when it involves a foreign target. But technically they are storing it regardless if you do or not, and we are basically trusting them to not look at it. This seems to be the biggest issue that is…
And trusting them not to lose control of the data. Given their inability to protect against Snowden, Shadow Brokers, etc. that is of course a reasonable possibility.
It's also a national security risk, imagine if an antagonistic foreign government had blackmail power over the US business elite, military officials, and politicians.