Interesting questions. I really wouldn't want a state where everything that anyone's been doing on (or over) the web in their lifetime can be dug into and potentially made public after their death. Not because it'd have to be shameful, but because it's private, and not meant for a post-mortem life either.
Another issue that's kind of related: who is going to take care of the judicial rights of the dead? Once the internet has been around for a couple more decades, and with more and more of our lives getting stored and pulled around online, it will become far easier than it used to be to spread sleazy, insidious and often false rumours about dead persons, especially those that are within living memory - and try to back these rumours and fakeries up with documents, often forged or doctored documents and pictures. If someone is spreading rumours or damaging claims about dead people - whether these are planted anonymously or published in the open right from the start - who is supposed to watch over it if it amounts to calumny and scandal-mongering? And how do we avoid that the entire field of journalism and (poularized) science and history could become a scandal factory? Rumours can be almost impossible to defeat even today, as it is, and the more the web grows the less chances there will be of decisively laying any such stories and claims to rest if they sound cool (to some people, at least). What hits off on the web isn't what can be shown to be true, it's what generates attention and has a "gee whiz!" factor.
At the same time, it's become much, much easier to forge and meddle with pictures and documents so that the changed artifacts look convincing enough to trick even educated newspaper readers, seasoned editors (giving still wider circulation) and even profesionals who know the real thing.
The answer used to be that you don't bother to smear dead men with sh-t and calumnious accusations, unless those are clearly relevant. There was a strong moral bar against it in the public mind and in the way publishers operated, but that bar is getting crunched away. - And because you had to get your thing past an editorial board - for a newspaper, a book publisher, a university or a record company, etc - a good deal of the worst indecencies and muck were stopped, in the past. But now you can publish cheaply on your own, you don't have to convince anybody anymore or listen if they'd say "you can't put it like this unless you have solid proof for it or you show me that it's useful to write that way otherwose I'm not helping you bring it out". The publishing hierarchy is broken, and that's pushing a higher demand for scandal stuff.We're going to need laws soon to protect not just the dead but the living.