Q:

How would the Four-Point spell help Harry find the center of the maze?

Spawned from a discussion in the comments of: Why didn't Harry use the right-hand-rule (or other methods) to solve the Triwizard maze?
In the 4th book of the Harry Potter series, Harry uses the Four-Point spell to supposedly know which direction to go in order to get to the maze:

Harry had soon mastered (...) the Four-Point Spell, a useful discovery of Hermione that would make his wand point due north, therefore enabling him to check whether he was going in the right direction within the maze.

How, exactly, would knowing which way is North help him to find the center?  He might know where the center is in relation to where he's started, sure.  So if for example he started on the southern edge of the maze, he knows he has to go north.  But then what?  He travels north for a while, or at least as north as he can go given the maze walls and obstacles.  At some point, he will have passed the center of the maze, and it will be somewhere south of him.  But he has no way of knowing when that happens.  He has no way of knowing when "north" is any longer the direction to be going, and is instead taking him farther away from the center rather than closer to it.
Forgive my exceedingly crude illustration: 

At the point he enters the maze, he can know he has to go North.  When he reaches a barrier, he randomly chooses to go left (West).  Then another corner forces him to go North again.  At the point of the dot near the North-West corner (assuming I was better at drawing and he couldn't actually see the cup from where he was), how would knowing which way is North help him to decide to go left or right?  It would only work if Harry knew he had already passed the point where the cup was directly East of him.  Without knowing that, there's no way of knowing if North or South is correct way to go.
Is this just an error in the reasoning by J.K. Rowling, or is there some fundamental aspect of compasses and mazes I'm not understanding?

A:

While the Four-Point Spell tells Harry where North is, he also has other important pieces of information:

the maze occupies the area of the Quidditch Pitch (an oval 500 feet long and a 180 feet wide)
the goal is to reach the center of the maze

How does he use this information?

At the get-go Harry knows the distance from his position to the cup (of course, the other champions know this too).
For example, if the champions enter the maze from South and the longer axis of the pitch runs N-S Harry knows that the cup is 250 feet North (this is probably not the case, but bear with me).
Now, Harry need to keep track of the distance he travels in the North-South direction and in the East-West direction:
For every step he is forced to take East or West, he knows he will have to later take a step in the opposite direction.
Moving North decreases his distance from the cup; should he move North more than 250 feet, he would have to start moving South when possible.
Every time he meets a fork, he can make a decision according to the cup's relative position (i.e. choosing the path that seems to go in the direction of the cup, or avoiding the one going in a completely different direction).

In order to have an (approximate) idea of the length he is walking, he can either count his steps or look at the end of the "segment" and estimate that distance (being a Quidditch player, he is probably quite good at it).
However, knowing the cup is currently 50 feet West and 20 feet South would have no use if he didn't know anymore where West and South are due to all the turns he took.
Vice versa, knowing where North is would not give him a clue if he didn't know the direction of the cup. So, the spell is a helpful tool, but it is not enough to guide Harry effortlessly to the cup (otherwise, it would probably be considered cheating).
Bottom line:
The Four-Point Spell tells Harry in which direction he is moving, so that he can correctly update his mental record of the cup's relative position.

