This is one of my absolute dislikes with both Facebook and Twitter - you pile all your data in there, they keep it all and own it all, and make it a royal pain for you to get at it again - even just for simple things like "I wonder when I was in XYZ?" or "What was that link that Matt posted last year?".
I haven’t seen a similar product for Facebook, but Tweet Nest (http://pongsocket.com/tweetnest/) is a step in the right direction for Twitter. It makes it easy to download browse, and search your tweets on your own server. Here’s an example (my own tweets): http://chasenlehara.com/tweets/ [Note: I have no affiliation with Tweet Nest, I just really like it!]
Nearly everyone makes the fundamental pagination mistake (Blogger being the sole exception), but calendar-based archives are a basic assumption that everybody implements. Facebook doesn't expose it in their interface but it's possible through the API. For Twitter it's completely fucked — the only people with access to your old tweets are the Library of Congress.
I imagine there are technical limitations leading to economic reasons for these kind of mistakes. So much data, sitting in so many massive silos, that they must design their systems on the basis of peoples' access patterns only hitting the most recent subset.
That, and the opposite economic reason - that you can charge for the older/richer/more complete dataset.
(EDIT: I know it's odd that I was whinging about the same thing a few posts up. I don't really know what the resolution is for that.)
I think the true reason is really just pervasive ignorance — everybody royally fucks this up and doesn't question it for a second.
If you have N items with M on each page, and the same request for 'page 2' always returns items N-M through N-2M, with the contents shuffling off the end as N increases, you're an abject failure. SELECT … LIMIT M OFFSET N-(P-1)•M is in almost every single web app and totally bullshit. It's incredibly depressing, but we'll probably be stuck with it for at least the rest of our lifetimes.