There are A TON of bugs with Multiplayer on Pocket Edition. We are both using iOS 6 on iPod Touch 4th Gens on a 6MBPS down 1MBPS up connection.
They all seem to be traced back to severe lag.

1. Ghost other player that isn't where the player is supposed to be (Ex: player is in house when on other client, player is outside)
2. Ghost other player gets punched, other player gets hurt.
3. Fall damage doesn't occur until a while after the fall. (Usually about a minute)
4. Chests don't open for a long time (About 2-5 minutes!)
5. Sheep, Pigs, Cows don't get hurt when a player hits them
6. Items take a long time to pick up
7. When shifting items in a chest, may take a while for hotbar/inventory to update.

My cousin and I enjoy playing this game, but these lag bugs make the game unplayable. Is it possible to change the way data is sent among devices to try to cut down on lag?