Similar problem, yes, but a bit different. If you want the entire surface of your mesh to be the same color, you can simply select the object in Object/Edit mode and click apply. However, in Object/Point Edit mode, you need to remember that color is applied to faces, not edges or points. This give you the ability to make different faces different colors. But you won't be able to actually see the color until you switch wireframe view OFF (i.e., to Flat or Smooth shaded).
By the way, I'll reiterate what's already been said --- this information is covered in the manual! It's a great resource, but only if you read it.
