Ack-Ack,
The original Beowulf poem consisted of the same three "adventures" that the film portrayed: Grendel, his Mother, and the Dragon. However the major difference, and it's been a LONG time since I've read any of the original poem, (I MUST pick it up sometime. I've been waiting for Tolkien's translation, but until the son kicks it and someone else takes over the family company it may never be published) is that the poem relies VERY heavily on some of the background legends/history of the Danes and Germanic peoples to establish its setting and world (specifically mention of some of the historical or semi-legendary kings, places and events of the 5th/6th centuries).
Really you can sort of look at it like, Beowulf is to Danish and Germanic legend what The Lord of the Rings is to the Silmarillion: One large tale set against the backdrop of a deeper mythology (that Tolkien was enamored by the poem, and one of the first to argue for Beowulf's LITERARY, rather than historical, merits has to play into this somehow). This IS sort of a drawback since contemporary audiences wouldn't understand the references like someone versed in that culture would (like, say, a mead hall in Saxon England) but I think Jackson's LotR illustrated that you CAN make these allusions without sacrificing accessibility.
This was a major failing of the film, because a LOT of that mythology was disregarded for cartoonish Hollywood spectacle, and much of the richness of the original legend was lost, which is really a shame. They had the opportunity to show so much of how deep and textured native Western European mythology was before Christianity displaced it, and gave it all up for cheap thrills and bawdy humor.
IMO, the best and most enjoyable part of the movie was the battle against Grendel, which if I'm remembering the poem correctly is the one part that's truly faithful to the epic (that should be a lesson, there. If it's not broke don't "fix" it). I also loved that Grendel's dialog was entirely in Old English. It's so far removed from Modern English as to be another language altogether, but at the same time is JUST familiar enough that you can almost understand some of what he says. There's something that's just hauntingly beautiful about hearing it spoken, and I wish they'd have used more of it.