I am having a similar issue with Ipad 2 latest IOS. From MBP to ipad, no issues from Ipad to my MBPs no photos.
After enabling photo stream on your ipad it should be automatic that any picture taken will upload to your photo stream but this is not happening.
Both the MBP and the Ipad are on the same wifi network and it works one way but not the other. I have no issue with accessing the internet on either the MBP or the Ipad....
Okay I just did a further test...guess what, I turn my cellular data off and took some pictures, worked like a charm.
So Ipad, IOS 6, Apple has an issue here in regards to wifi and cellular data both connected...
Need others to verify this, if your photos are not appearing in your photo stream on your ipad after you have snapped them.....try turning off cellular data and then retake them again and see.
Cheers
James