If my actions in an earlier part of the game would affect NPC dialog with me and others (This occurred in Oblivion, like when you pwn the Grey Prince), then how about hearing something about what your characters did in previous games, like hearing tales of the Champion of Cyrodiil smacking deadra around and helping Martin deliver a back-handing of biblical proportions to Mehrunes Dagon (yes, I was laughing at this while I typed it) and tales of the Nerevarine drinking Daggoth Ur's sweet, sweet tears of defeat. The moral decisions (based on fame and infamy) would play into the dialog as well as the race gender and class of your character. This data could be pulled from a saved game, cemented into a part of your Skyrim save, and the previous character could be brought up in rumors.
To clear up any potential problems:
1.) Your latest save would be used.
2.) If you don't have a save, the game defaults to a male imperial adventurer who did a ton of good (like default is 9001 Fame and 0 Infamy).
3.) Random quests and how they were completed could be used (though I highly doubt it would be possible).
That's all the potential problems I can think of, but if anyone thinks of anything else, let me know.