Set dimensions of a mesh I've set "Meters" as the unit I want to use, with a 1.0000 scale, which means that every square on the grid is 1 meter, right? 
Now, I want to set a cube to be exactly 1.5m tall (for example), how do I do that?

I tried to set the scale in the "scale" section in the object tab, but there's a problem.

This is with scale set to 1 on every direction:



You see, it takes up 2 squares on the grid for each side. I mean, look at the top side, it takes up 2 squares. If every square is 1 meter, it means that the top side is 2 meters long, right? 
If I want it to be 1 meter long I have to se the scale to 0.5, like this:



The point is... I've set the scale to 1.0000, as I said, so 1 should be 1 meter...
Did I miss something or this is right?
That's correct.

The scale is an arbitrary number which is used to offset the size of the mesh from it's original state. It doesn't refer to the actual size of the mesh, just how much bigger or smaller it is.

I think you are looking for the dimensions values in the properties region:



Setting the dimensions will set the scale values to the appropriate value to make the mesh a certain size, e.g. 2.5m tall: