How do I get my application data back after OS upgrade?

Question

First I tried to update to iOS 5.1.1 by downloading the .ipsw file from Apple and shift-clicking the Update button. I got Unknown Error 3014, which apparently is a known error and is to do with contacting the Apple server. So I tried again, and this time the iPad got stuck in the "Connected to iTunes" screen, and I searched online and found that the only real way out of this is to do a Factory Restore to iOS 6. Oh well, I would have to put up with the new Maps app but that isn't too bad.
So I did that, then I selected to restore"Phil's iPad" onto it, but my machine ran out of disk space. I cleared up some space, and got it to restore again, but I think that what happened in between was that it automatically backed up and synced the new half-restored state to my PC. So when I came to restore it, it only restored half of it. Since I had iTunes set up to sync every time I connect, the system that keeps the most recent three backups had deleted all the backups that were of any use and all I ended up with are three backup states that are all missing my application data. All my game progress is now gone, all my photos and home videos, all contacts, notes, all gone and I think gone for ever.
Any idea whether it's possible to get all my stuff back?

Answer 1

All apps and media should be in iTunes on your computer, if you've failed to transfer purchases from the device to iTunes it is possible to download past purchases.
Downloading past purchases from iTunes
Contacts and calendars are in whatever application on the computer or cloud service you have configured them to sync with.
Pictures and videos taken with the device are designed to be copied off to the computer regularly.
Frankly, it is not very smart to rely on a device that can be so easily lost, stolen, or damaged as sole storage of your imporant data, I'd dare say it is boarding on completely moronic.