I am having a similar issue.
I'm not sure if it is due to the iPhone 4 or iOS or if this is a Verizon issue.
On my 3GS, my sister could receive pictures via MMS from me. Not now on the iPhone 4 -- she gets a blank message if I send her an MMS picture.
Oddly enough -- I chose a picture I took with the 3GS and sent it to her from the iPhone 4 and she received it. But if I send one taken from the iPhone 4, then just a blank for her.