In the last scenes, Wun Wun walks towards the sea, heading to the ship, but he disappears right after: as the cameras feature the boat moving towards the ship, Wun Wun can't be seen anywhere on the water. He simply vanishes.
As Jon and Tormund run to protect the gates against the Army of the Dead, Jon runs towards one of the wights and sticks his sword into it, then the camera changes to back view and we see Jon a few meters back, running again towards the same wight.
When Jon kills a White Walker, it starts shattering into ice before it is touched by the sword. The sword is more than a foot away from it when it starts to shatter.