According to documents reported on by the German newspaper Der Spiegel, the NSA has a fool-proof and covert method of remotely installing malware onto iPhones. Senator Ron Wyden has warned publicly that the NSA has these capabilities, though he didn't name Apple or iPhone specifically. Previously, Der Spiegel reported that the NSA internally referred to iPhone users as "zombies" who "pay for their own surveillance."
The newly disclosed malware tool, which the agency's Tailored Access Operations division calls DROPOUTJEEP, enables the NSA to both extract and implant information onto the Apple smartphones. It also allows analysts to turn the microphone into a hot mic, enabling the NSA (and perhaps also the FBI, CIA, etc) to listen to what's happening in the room when you aren't making a phone call. Worse still, it grants the NSA access to your text messages, contact lists, voicemails, geolocation data, and cell site location information. Finally, it also allows the NSA to take photographs of you using your iPhone's cameras. (If you don't want spies looking at you while you go about your daily life, you should put a piece of tape over the front-facing camera, at the very least.)
See the slide about DROPOUTJEEP, from this talk by security researcher and journalist Jake Appelbaum, below. The NSA documents describing DROPOUTJEEP boast that every attempt to implant the malware on iPhones will always succeed, Appelbaum reports.
What say you, Apple?