The Minecraft window favicon appears 'corrupted' on Linux platforms - i.e. the crafting table icon is scrambled beyond a certain point.
I've tested this on Debian using both the GNOME and XFCE desktop environments, and Fedora using GNOME. Each shows the same bug, but with a slightly different corruption for each.
The attached image shows how it appears on a Debian computer running XFCE 4.8.
And yes, I have tested it using Java 7 instead of 6 - same problem.
Can confirm. As a side note I recommend you avoid using OpenJDK 1.6 with Minecraft as it has been known to cause issues. Either OpenJKD 1.7 or Sun/Oracle java is my recommendation.