DIALOGUE. Check some of the Kenpachi vs. Nnoitra chapters for example. I dare you, do it, and read what the characters are actually saying. It'll make you puke blood. Scenes are ruined because of the lame crap the characters are uttering. Not that, for instance, this one could have been "cool" at all anyway, but it's a good example about the whole dialogue thing.
Other than that, the story doesn't proceed at all, as most people probably have said, because even the most insignificant fights take a dozen chapters in the least. Reading the longer and more important fights simply destroys brain cells; it's not really an exaggeration to claim that there's not a single fight in the entire series that doesn't go like this:
1. Hero and villain meet for the first time. The villain is like the strongest person in the series at that moment and the hero gets his ass handed to him, except that the villain doesn't kill him for some obscure reason.
2. Since the hero survives, he somehow powers up with sheer willpower, and marches back at the villain's feet to challenge him again.
3. The hero proves to having gotten stronger than the villain appeared to be when they last met, due to the nonsensical powerup in 1) -
4. - and thus the villain "gets serious" and totally destroys the hero once more.
5. No mind, he failed to kill the hero again, who thus has enough time to somehow level up again, and kick the villain's ass.
6. And so, the villain receives his power up technique as well.
7a. They both pull their strongest special techniques out of their asses, clash, and the hero narrowly wins
or
7b. The villain's new powerup is too strong and defeats the hero, so a new ally appears out of thin air in a supposedly very cool scene and proceeds to fight the villain in a similar way (see 1-6) and eventually wins.
8. As the hero (and in case of 7b happening, the new ally) is overjoyed by the fact he actually pulled off the victory, a new enemy, hundreds of times stronger than the one they just faced, appears and totally kicks his ass -
9. - except that the hero narrowly survives, so he can power up and face the new threat again in a couple of chapters.
And yeah, there's no real plot. The author seems to be drawing the panels on a whim without any script to follow at all. I've seen better storytelling in 3-panel newspaper comic strips.
I'm trying my best not flame and not to mention other shounen series at all here but it's proving more and more difficult.
edit: tried to fix some grammar but it's still a mess. And yeah, I did somewhat like Bleach in the beginning, I enjoyed Kurotsuchi's recent fight and I still do check the new chapters every month or so.