I had a hilarious experience with this issue tonight, but unlike 2729 I think this is a case of something NOT happening on the server when it should.

When you attack another player the server should verify that the axe/bullet/whatever actually hit the person. It seems right now that the server just accepts the message from the client that the attack was successful, even though the victims latest position can be far away from the position that the desynced player sees.

Now, for my story:
I was heavily desyncing when in a group of players that I was also on teamspeak with. On my PC I saw them standing still in a house, but I knew they had moved on from there. In frustration I punched one of them in the head a couple of times. Then I hear on teamspeak how one person in the group had suddenly become unconscious just as they were walking along the road, with nothing attacking them.

There was a lot of confusion about what might have happened. Was it that rotten orange from 2 hours ago? Was he too thirsty? After a few more 'incidents' of this nature, the group decided that the town was haunted.