When in SMP, other players cannot see when you change the item you are holding i.e. the held item does not refresh until you reconnect

When you hold an item, it displays you holding it in third person. The item changes when they switch to another item in the hotbar.

When I was playing, it would only show the item each player was holding when you connected to the server, and NOT change when they switch to another item

1. Start a server
2. Join 2 players
3. Look at each other and switch items in the hotbar