The hypothesis put forward in the NOVA feature is that non-REM dreams are focused on honing skills we are learning in our daily lives, and that REM dreams are focused on putting those skills to the test in hypothetical situations.
Therefore, REM dreams tend to be more negative and more often nightmarish.
I'm not so sure about that last part - AIUI we all dream more than we remember, and we tend to better remember the dreams we wake from (during). In my experience, I'm far more likely to wake during a disturbing dream than a pleasant one (lucid dreaming aside). If this is true of other people, an overall excess of disturbing dreams will be remembered/reported, even if they are in the minority of all dreams.
I only get disturbing dreams if I'm too hot in bed - it seems to be the way my subconscious wakes me up so I can cool down.
I get three different 'levels' of conscious awareness in dreams - fully lucid, where I try out things to see what will happen, and which are fairly rare; then there are observing dreams, where I am aware I'm dreaming, but don't interfere with the 'plot'; finally, the implicit awareness dreams where I'm not fully conscious of dreaming, but I know I have an extraordinary power - usually levitation - that isn't a 'real-world' possibility. One consistent oddity about levitation dreams for me is that no-one in the dreams takes any notice...
One useful trick I use if I'm unsure that I'm dreaming, is to try to read something - a poster, newspaper, book, or jar label. In dreams, the text is different every time I look at it, and sometimes it makes sense and sometimes it doesn't. This can be enough to trigger lucidity in a dream. It's a bit of a Matrix-like effect - as if the dream resolution and rendering isn't fine enough to make text consistent and readable.
ISTR in somewhere in Carlos Casteneda's Don Juan books, he suggests that to stabilise and refocus a lucid dream that's breaking up, you should look at your hands. It's worked for me once or twice.
Over the years, I've noticed a strong consistency in my dream environments, familiar dream places, buildings, & situations - but few of them closely match real-world places. It's an alternate, virtual reality; only the people are common to both dreams and reality. I sometimes discover that something I think I remember as a real happening turns out only to be possible if I had actually dreamed it - a strange realisation.
I strongly suspect much of the supernatural and paranormal woo that seems to be such a powerful lure to many people, originates in dream experiences. The natural ability to tell dream from reality is pretty effective, but the boundary is leaky...
