Graphics are not displayed properly on Mac OS X 10.9 with ATI Radeon

Hello,
I made my first Unity game for Mac OS and it is working nice on my mac mini with Intel HD graphic card. I sent the game to friend of mine to test it. He has a mac with ATI Radeon video. On his machine the game looks so bad. The texture of the main game character is not displayed properly - the different colors of the texture are not positioned right. Another issue is that bonus objects are visible through the character. Can you tell me what this problem is related to? Is this a driver issue or problem with Unity?

OS X 10.9 with a Radeon 5870 here, no issues.

–Eric