The anime stayed very close to the manga up to the end of the Rescue arc, so you can probably just jump right in at 182, when they get home. Actually, I'd recommend picking up at 179, so you get the manga version of the Byakuya-Rukia backstory and the talk between Renji and Byakuya, which are just a bit different. *hearts the manga*
In general, the manga offers more detail and more depth, though there are places where the anime went and made shit up. Most of Soi Fong's actual experiences with Yoruichi, for example, are anime-only. Also, interestingly enough, the anime added to /both/ the Rukia-in-Rukongai sidestory /and/ the Rukia-and-Renji-in-school sidestory. In the first, they add more stuff about how she has more spiritual power than Renji; in the second, they add stuff about her being worse at school than he is. The manga has her in the same classes as Renji, it's just /socially/ that she doesn't make the same connections.
no subject
In general, the manga offers more detail and more depth, though there are places where the anime went and made shit up. Most of Soi Fong's actual experiences with Yoruichi, for example, are anime-only. Also, interestingly enough, the anime added to /both/ the Rukia-in-Rukongai sidestory /and/ the Rukia-and-Renji-in-school sidestory. In the first, they add more stuff about how she has more spiritual power than Renji; in the second, they add stuff about her being worse at school than he is. The manga has her in the same classes as Renji, it's just /socially/ that she doesn't make the same connections.