Just to throw another point of view on cheating in the ring here...
I know that playing Dominion online and playing Dominion in real life (IRL) are two totally different things.
But there's a part of me that really wishes it were possible - just as an option - to emulate the IRL experience online.
Case in point - the log and the VP counter.
As I understand it, the reason that the VP counter is always on is that because the log is always 100% visible all of the time. There's nothing stopping a player from simply going back through it and counting up the points themselves during a game. And that makes some sense.
However, I feel that using a VP counter kinda violates the spirit of the game - kinda like cheating. IRL, the game is played by humans sitting at a table with no notebooks or record-keeping. It's up to the players themselves to keep track of what's going on during the game, turn by turn.
Part of the fun of certain VP cards/landmarks is that there is practically no way for one to know what their or their opponents' score is, other than a rough guess. (think Vineyard, Museum, Fairgrounds, Fountain, etc) I'm not saying it's impossible to keep track, but unless you've got a very good memory, it's not that easy.
I think it is critically important to have a thorough log of exactly what a player did on his last turn readily visible to all other players, because sometimes people play super-fast ("what the hell did they just do?") or sometimes you have to step away from the game for a moment ("okay, what did I miss?").
But to be able to scroll all the way back thorough to the beginning of a game while that game is still in progress - I think that violates the spirit of the game.
I don't think it's impossible or unreasonable for the log to only show the actions of the previous turn - in specific detail, to the other folks on this thread's points - and to keep the remainder of the game (from the turn before last through to the beginning of the game) hidden until the end of the game. In fact, I feel like I might have seen this in an earlier online iteration of the game in the past...
Long story short, I think the log should be as rich and detailed as possible (for post-game analysis), but during the game it should only be used for seeing what your opponent(s) did during their last turn.
And in the case where both players decide that they want to be able to look back through to the beginning of the game (or they both agree to cheat), then that should be allowed, as an option.
But I don't think it should be the default way to play, as it is now.