Like many people, I had problem installing iOS 5 on my iPhone and iPad.  I got error 1654 when I tried to install iOS 5 on my iPhone and iPad 2, while I got error 3002 when I tried to install it on iPhone 3GS.

Some forums and websites suggested to remove other USB devices, restart the computer.  I've tried on Mac and the PC but I still got the same errors.  Finally I figured out the best solution:

• First, make sure you downloaded the latest iTunes (10.5)
• Second, do a full backup for your iPhone or iPad by right-click your device in iTunes then select "Back Up".  Note on the Mac you can also use "control-click" or "two finger click" then select "Back Up".  This may take a while depending on how much information it needs to back up.
• Third, after the back up is done, click "Restore" instead of "update".  This will reset your iPhone or iPad to factory setting, erase everything, and then install the iOS 5 automatically.
• Finally, after your iPhone or iPad has finished installing the iOS 5, it will automatically ask you to if you want to restore settings from backup: just click Ok.

Please be patient with the installation and restoration.  It took me 4 hours to install iOS 5 and restore all my settings for my 32GB iPhone 4.

Good Luck!