I love the game, and though there are a few differences between this version and the dice game version that I'm not entirely happy with (e.g., 3 doom tokens at once, the different way that Spells function, etc.), I still really enjoy it. And I like the idea of a scoring system being added, but unfortunately I think it's kind of a pointless one.
As it is, you get more points if you have more turns and more completed adventures and such. But to me, a reflection of better play would be if you completed everything sooner and more efficiently. The sheer number of things completed doesn't necessarily reflect good perforance. The best score I've had (close to 6000) was in a game where I failed a lot of adventures and tasks and barely eked out a victory, but because of that I was able to get more total monsters killed and more overall tasks completed and more Other World adventures out there and such. But really, it was a pretty sloppy game, and there have been several other games where I made better decisions, was way more efficient and generally kicked ass with much more authority, but didn't get nearly as many points. So, in that respect, the scoring system doesn't really represent anything meaningful. As it is, too many things that score points are completely abritrary... For example, Elder Signs are scored, and normally they'll be 14, but if you happen to get lucky for an opportunity to complete Ryleh for the win when you already have 13, then you'll end up with 16 for the win, and 200 extra points. But that could just be dumb luck to have that opportunity available, and in another game you might have played a lot better but only had the chance for 14.
Considering the game is adapted somewhat from Arkham Horror, perhaps a scoring method could be adapted from there. For example, I think that unspent trophies should be of some value, as they are in AH. Purchased Elder Signs should be a negative score, IMO. And the number of doom tokens left to add before your victory should have a much higher value (as it is, that is represented in the scoring system, but it doesn't mean that much as a whole). The number of turns should be weighted more as a reverse value... the fewer you had the better, as long as you won. I think the number of investigators you start with should be a base score, with fewer scoring more because there's more danger of loss when playing with only 1 investigator (though that's balanced somewhat by them getting all of the trophies) and there are fewer opportunities to assist with fewer investigators.
Anyway, I'm not sure what would make the best formula for representing the true value of how well you did, but as it is, it really doesn't seem to capture that at all. Here's a list of what I think might be most reflective of performance for a victory (I don't think a loss should even be scored), with some suggestions for relative weight.
Starting with 1 investigator: +3
...2 investigators: +2
...3 investigators: +1
...4 investigators: 0
Unspent trophies: +X
Unused items: +X
# of doom tokens left before Ancient One would have awoken: +X
Purchased Elder Signs: -X
Devoured investigators: -X
Completed tasks as a percentage of the total number of tasks: +/- (not sure what the threshold should be... maybe if completed is at least 75% or higher, then you get a bonus for that, otherwise it's a negative)
Number of monsters killed as a percentage of the number that appeared: +/-