I don't think the dreams are completely crucial (a critic who's seen episode 3 mentioned cryptically that Bran's dream "is and isn't" in this episode, so there'll be something--maybe just Bran mentioning it?) but now that you mention it, it does make me a little worried for the future fantasy elements. One of my favourite bits in the books is Dany's visit to the house of the Undying in Qarth, which should play out like a freaking David Lynch movie on screen. The dreams in S1 would have made a good trial run for seeing how the filmmakers handle the fantastical stuff down the road, which tends to have a dreamlike quality in the books--I'm also thinking of Mirri Maaz Duur's spellcasting near the end of book one. But I'd hate to think that they're so committed to "gritty and realistic" that they're going to minimize this stuff entirely--this IS still a fantasy series, after all. (OK, the White Walkers were really well done, so that gives me hope.)
OK, I gotta go back to Dany again. I actually haven't seen the second episode yet, but it sounds like this whole business is getting pretty controversial, with a number of people saying they turned away from the series in disgust due to what seems like misogyny and racism. Apparently Dany's feminist sexual awakening is coming off more like Stockholm Syndrome to some people. On the one hand, I appreciate that the filmmakers are playing a long game here, and they need to set up "innocent white girl raped by scary brown savages" so they can subvert it later, which will require patience from the audience. And of course, the brutality and limited options of medieval life is part of the point of the series. But on the other hand, given the producer's bad choices (IMHO) in their portrayal of Dany's wedding night, and the fact that the series doesn't have access to the book's internal monologues, I'm not sure that this storyline is going to prove satisfying and subversive enough to win these people back. In particular I'm not sure Khal Drogo and the other Dothraki are going to ever seem likeable and three-dimensional enough to overcome the racist first impression they gave in the pilot. And the later storylines could very easily turn into an unfortunate "Danaerys, white queen of the savage Dothraki!" cliche. I'm not sure Benioff and Weiss are capable of handling this delicately enough, especially given the rather crowded seasons we'll be getting.