Is momentum and energy conserved?
See Niven's article in either Playgrounds of the Mind or N-Space where he discusses the various ramifications.
If you go east you arrive with an upward velocity relative to the surface and bounce into the air. Going west you are moving into the ground. Going north or south you arrive moving sideways.
What if your destination is higher than you are? Where does the energy come from? If lower, where does it go?
How much can he take with him? Does he arrive naked? Especially when learning?
If energy is not conserved, Can he step into a lake, and teleport himself and the lake to much higher lake that supplies a mill?
If he's fast can he teleport a large mass of water (or a big rock) above a castle and teleport back?
If he knows a location and can visualize it precisely can he go there directly (aka Pern's dragons)
What happens if there is something there when he arrives? E.g. it's raining? (You suddenly have raindrop sized chunks of you that have twice the density. Any idea how much energy is stored to compress water to twice it's density?)
Is there a thunder clap when he leaves? What about the air when he arrives? Or does he just swap places with a volume at the destination?
If so, can a non teleporter move in the counter direction to a teleporter by standing at his destination?
If he can counterteleport, this gives him another way to fight. Go to the neighborhood of the enemy castle. Teleport into the air above the castle. Teleport into the wall. A statue of himself appears where he was. A several hundred pound statue of himself falls on the castle. Rinse and repeat.
Suppose it takes longer to 'recharge' between jumps. Is there an advantage to building towers with shock absorbers that will allow him to take longer jumps?