Yeh, the story and storytelling is terrible.
I still haven't finished the campaign, and this could be rose tinted glasses, but I swear the original game wasn't as bad story wise. This is passable, but I feel like somewhere in the last decade Blizzard's writing quality took a nosedive. It's not Michael Bay bad, but I don't feel like this game grabbed me in the same way SC1 did.
I think the biggest issue I have is that the new characters don't add anything to the story (Tychus, the science lady, and Tosh are just props to provide motivation for the missions), and all the mystique over the original characters was pretty much handled in SC/BW. There's really nothing new being covered. Which I guess is to be expected since this is the first act in a trilogy of games, but this is probably the longest I've seen a story just biding time until part 2.
That said, the best cinematics are the ones for the "non-canon" endings for the ending of each plot arc.
Levels are still cool. Just the parts that connect them are mediocre. At this point I'm expecting Diablo 3 to have the same problem: meh plot/writing, fun gameplay.