Why is the battery on my Iphone 5 weak and half of the screen has a blue tint?

The battery doesn't even last a 1 day! And i'm not actively using it either. After holding the cell between my shoulder and ear for half an hour the right part of screen has a dark blue tint and it doesn't go away. WTF

Go to Apple, they will determine the problem. If it is defective, you are entitled to a new one.

All the iphones have bad battery life. I had to charge mine twice a day usually. But the screen issue you described only happens with the iphone 5 because its built cheaply. I would recommend the iphone 4, its the best one.