Have you ever had the though that something isn't right, or that you may be dreaming, even though the script of the dream continues?

What you may need is a certain action that will break the dream plot. It can be very simple.

Next time you think something is weird, look at your hands. Keep that in mind before you go to bed. "Next time I am dreaming I will realize I am dreaming and look at my hands." By looking at your hands you are preforming a conscious action with intent, and this can be enough to take your focus away from the plot enough to make it stop. I would be like floating down a river (the stream of the dream plot) and then deciding to grab a hold of the shore (intent to look at your hands.) You need an action to preform, or you may continue to just keep going along with the plot even if you realize something might be up.