When in first person, sections of the sleeve layer which are facing away from the camera (the end of the hand, the side next to the body, and the back of the arm) are not rendered.

Steps to reproduce:
1) Download this skin: http://i.imgur.com/LRmVBI5.png
2) Apply it to yourself at https://minecraft.net/profile
3) Start up the game and look at your arm in first and third person. In third person, the red border around your arm is clearly visible from the front, but in first person it is completely absent.