Sometimes a key such as "move forward" ("w") will get stuck, i.e. Steve will keep moving forward even though I have let go of the "w" key. The only way to stop Steve from going forward is to briefly press "w" again (walking into a lava pit also seems to stop Steve from going forward).

I think this happens when you are pushing keyboard and mouse buttons simultaneously, such as when moving while hitting mobs. Somehow Minecraft is missing a keyup event. Moving around killing endermen on DocM's enderman farm seems like a good way to reproduce it, but it seems to occur somewhat randomly.

This is an old and much-discussed bug: https://www.google.dk/search?q=minecraft+%22stuck+key%22 . See fx http://www.minecraftforum.net/topic/1153323-minecraft-stuck-keys-issue-solution-needed/ - but the much adviced "solution" of upgrading lwjgl doesn't fix it for me.

I also about as often have the problem that a keydown event is missed. Seems to occur in the same situations.