Most things such as certain quest that cannot be completed, missing npcs, being stuck in an area, missing items, etc can be easily fixed through the console command. Unfortunately console users don't have this luxury but... What a lot of people don't know is you can actually transfer save across platforms. Yes! You can transfer your Xbox save to your PC, fix/edit whatever you want to, then transfer the save back to play on your Xbox. This would also mean you either need to obtain a copy Skyrim for PC or just find a friend that has the game on PC.
I won' go into details here on how to transfer the saves, its quite easy and you can read about it here:
http://gamethingdaily.com/2011/11/19/xbox-360-skyrim-saves-transferrable-to-pc/
Keep in mind:
That when you do edit stuff on PC through console command do it through a unmodded Skyrim client or you risk things bugging out when you transfer the save back to Xbox
Make back ups of your saves before you edit them!
This will not fix coding bugs, such as textures, weird AIs, back pedaling dragons... etc

