How can you tell if an iPhone camera photo has been fully uploaded to the Photo Stream without using a computer?
In the photos app, you should be able to compare between the "camera roll" and the "photo stream" in the albums tab.

The picture shouldn't appear in the local device's Photo Stream until it is uploaded.

To see this in action, go to the Albums tag. Take a screen shot. (Power + home)
The photo will appear in the Camera Roll and (net willing will within a few seconds) then appear in the Photo Stream.