I do believe that they dream only because at various times I've noticed my dogs acting in various ways; sometimes they would act as if they were running, other times they would just have mouth/head movements, and other times they would bark in their sleep.
If you want to "see" a dog dreaming watch "Hatchi".....for a dream that will make you cry, no matter how strong you are.....
Jack and Taz definitely dream and do twitch in their sleep. Jack not too much anymore. He mostly grumbles and growls LOL! Now - Taz twitches a lot. Her little front paws start moving. DH calls it "chasing rabbits". She also talks a lot - it's mostly grumbling, moaning and groaning (really loud). It's funny to hear her. If she gets too loud and twitches too much we'll wake her up because it sounds then she's having a nightmare of some sort.
Sorry....it's "Hachi - A Dog's Tale" with Richard Gere.