I was actually going to suggest this myself, although it would have to be limited in some way since the full Elder Stats profile for a character has one page of Skills followed by six pages of Stats for Skyrim characters! A lot of the Stats are also not hugely important - does it matter exactly how many Potions a character has made?
I would suggest that the Skills page would be the obvious place to start for both Skyrim and Oblivion characters.
However, I would also suggest that, seeing as there's only one programmer adding new features to the site, adding a Character Update History
might be less important than getting support for Legendary Skills in Skyrim, and adding Morrowind characters?
Right now I take a screenshot of my characters' stats whenever I update them in Elder Stats. For example, here's my character Martin at:
level 70,
level 75,
level 77,
level 80,
level 82. (Unfortunately, those aren't his true stats because he's reset Enchanting twice, Smithing three times, Light Armor once, Speech once, Alchemy once or twice (can't remember), and Lockpicking once.) However, in theory it's possible to keep these screenshots and then input the data you care about into a spreadsheet program at your leisure, and even get it to do things like plot graphs.
It's important that in making a suggestion for a big feature, we figure out what we actually
want. What are we thinking this Character Update History should look like?
I was thinking that perhaps, each time we make a change to the stats, the site could somehow produce a text-only file which would automatically form part of a character's journal. Then a player could copy these files to their own computer and track changes in every single attribute and stat without bloating the site out of all proportion. How easy it would be to do this, I don't know. It really depends on the Elder Stats' internal database structure.