When using the "Loot all" button on the loot frame, it will automatically loot all items up to the first non-single stack, at which point it will stop and ask how many items the player wants to get from that stack.
As long as there is space in the inventory, "Loot all" should just do exactly that, taking all the items from the stack and continuing on to the next stack.

Just so I don't forget : Failing to loot because inventory is full shouldn't show "Looted [Item] x 0" in chat.