It would be nice for Mojang to update the shipped version of LWJGL to the latest version. I've had no problems what so ever with LWJGL 2.9.0.
The version of LWJGL shipped with Minecraft 1.6.2 is too old to support Mutter (the window manager used in most Linux distros). Upgrading the LWJGL jars and natives to the latest version (2.9.0) found on the LWJGL website fixes this problem. There is a tutorial on the Minecraft Wiki that shows you how to do this.
I didn't read the Wiki page properly. 1.6 has got 2.9.0. The only other solution I could think of is to make sure your graphics card drivers are activated and up to date (Nvidia cards are a problem).