I personally have been going through an experience which is almost the same as yours. Though, it will be an entire day of school or work in my sleep. It's as if I feel every second tick past as I watch the clock on the classroom wall. School will finish, I will drive home, go to sleep, wake up and I'm in reality. It's as if I am literally doubling my days significantly. And as you said, they become random memories. Going up to your mates and explaining a 10 minute conversation you had with them yesterday, only to realize the "yesterday" conversation was in a dream, is quite embarrassing.
So yeah, it's sometimes fun. But getting yelled at in work or school, getting in trouble or failing in report cards in dreams. Really does have a downside to my confidence and personal memories. Example: I have a dream in which I get higher than average percent score in my report card, go to sleep, wake up and go to *real* school to receive something just average. Makes me feel like a complete idiot. :/