Contacts and notes are designed to be synced to a supported application or a cloud service, simply sync them back.
Pictures taken with the device are designed to be copied off the phone regularly and then synced back via iTunes, again, sync them back.
Sounds like the device has not been used as designed.
Attempt to restore the device again using the same backup. If the content does not restore, there is simply nothing that can be done.
I also tried to update my wife's iphone 4 today. First it said iTunes needed to be updated, so we did.
Then iTunes said it was backing up her phone, and then updated it, and then needed to restore it, and it hung up while doing that. I left it over an hour, and the status bars (on itunes screen on computer, and on iphone) didn't move at all. So I shutdown and disconnected. Then I tried it again on my pc and got to restore window, but it wanted to restore MY iphone or our ipad, didn't have my wife's iphone info anywhere, even though it previously identified her phone and said it was backing it up, etc. So left with that choice (1 phone not working at all since it wasn't fully restored, or 2) restore it as MY phone or our ipad) we took choice 3, and tried to restore on my laptop,which had previously been used to back her phone up. Again, that didn't seem to have any info of her phone from a previous backup on the laptop. So we ended up, going for the laptop itunes process, which looked like it was going to wipe the phone. Initially we were optimistic since it looked like all her apps were going back on, but when it was finished ALL of her contacts, notes, and photos were gone. Gone.
Any help appreciated.