After I've played a game for a while I look at the reviews here on Gog and try to see which ones are helpful to me, and note the name of the person who wrote the reviews so i can get a feel for a reviewer and know if his/her tastes coinside with mine.
Next to the reviews is the line "Was this review helpful to you?" and the yes/no buttons BUT next to that it says (x users agree with this review).
So what does clicking YES actually do? Does it increase the 'x number of people who agree with this review' bit?
I read reviews that I don't agree with but that are helpful to me, What do I click? Can I not show my support of the reviewer without agreeing with the review?

As far as I know that "yes/no" option is the only way to rate a review and yes it does increase that "people who agree..." number.

Semantics. Click yes. :)

I told the staff about this back when the site started, but they never changed it.

Don't have much to say about this, but that's a good idea. Not the change the buttons thing, but the track down specific reviewers who have a taste similar to yours. I've found a couple of well recommended games to be not so fun for me, simply because it's not my style of gameplay or game, not because the game itself is terrible.

Don't click anything. If the review was erroneous then that's one thing, but if your personal tastes are different then leave it be. The agree/disagree options increase or decrease the prominence of the review in the list, so it does have an effect.