There is a difference between DFU and Restore mode.
While most people don't know it, this difference causes the "Error (1)" in iTunes trying to downgrade to 1.1.1 after accidentially updating to 1.1.3.
The big difference between DFU mode and restore mode?:
DFU mode doesn't boot up the "mac os" on iPhone - therefore it doesn't communicate with iTunes "as much" as in Restore mode and iTunes can't decide to interrupt downgrading the firmware etc.!!
The restore mode is the one everyone tells you to use (with iTunes icon etc. at the end) while DFU mode works this way:
1. Connect iPhone to Mac/PC - keep iTunes open
2. hold down power and home button
3. wait until red slider appears to shut down iPhone, keep holding down the buttons, count 4-5 seconds (while iPhone shuts down)
4. release power-button, keep home button pressed (there should be no Apple logo! If it appears, you waited too long to release the powerbutton - try again )
5. wait 5-10 seconds - iTunes should then prompt that there's an iPhone connected in "restore mode" - but it's different!
Now at this point even with iTunes 7.6 you can downgrade to 1.1.1. without errors.
While you usually startup the system with the known method with iTunes icon etc. this way the iPhone doesn't startup and iTunes can't actually regret downgrading.
Greetings and thx to the german site macbug.de