Keys get "stuck"

Sometimes (seemingly randomly) the game behaves as if a key is being held down when it isn't. E.g.: W, A, S, D, Shift, and Command on Macs (this manifests as a problem when deleting text in the chat because Command+Backspace deletes entire words at a time on Macs).

This bug affects Multiplayer as well as Singleplayer (ever since Minecraft was changed to run a local server for Singleplayer).

I thought 1.6 brought an updated LWJGL version which was supposed to fix the issue, but it hasn't.