Playing offline split screen in a 200MB world. We experience a fair amount of delay between each button press in the inventory screen. This lag affects both players as the whole game takes about a second to register the click. This happens when: crafting items, moving items to or from containers and the inventory, opening the inventory, selecting an item in the inventory, and dropping an item in the inventory.
Since the April 3 update, this lag seems to have intensified greatly except when both players are in the same chunk. In that case there's almost no lag at all, and inventory functions feel fine. It's only when the players separate that the lag comes back.