If you’re having problems restoring your iPhone, iPod and keep getting one of these 16xx errors, the solution might be much simpler than you think!
The iPhone could not be restored. An unknown error occurred (1600).
There are numerous reasons for running into these errors – one of the simplest (and least obvious) fixes for it is re-enabling your Apple Mobile Device and iTunes Helper services. These are both services that start when you’re booting your machine – and if they’re not running, the restore won’t work (because they let iTunes know when your device is plugged in).
I disabled/killed them because they were eating resources, and I rarely use iTunes – but apparently they’re necessary for restoring.