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Imagine you teleported a gallon sized chunk of Venus's atmosphere onto the top of your desk. What would it smell like? Should you avoid breathing it?
If you didn't compensate for any pressure difference in teleport, would there be a boom of a high pressure chunk expanding? Or a woomph of a low pressure chunk getting crushed by your local air pressure? Does it matter what part of the atmosphere you got it from?

How about a hunk of the sun? Would you notice its arrival?

If you stuck your arm across your desk and into Mars's atmosphere, what would it feel like?

You can vary what teleport compensates for.
Does Venus atmosphere arrive still with Venus's orbital velocity, or has teleport compensated and made it arrive stationary.
Is incoming stuff magically contained? Contained by something physical? Not contained at all?
What happens to a plastic coke bottle some vacuum is teleported into? The steel safe which gets some solar core? (Does it explode or melt or both?)
Say you compensate for pressure but not temperature.
How does the bottom of the ocean feel? What can you grab?

But he has momentum being preserved across teleport. So if you are falling when you enter teleport, you are still falling when you arrive.

Consider the spinning earth. As you stand on the earth you are moving east at a few hundred m/s [Discussed below]. Say you teleported east half way around the earth. You come out at ground level. You are going a few hundred m/s. But the planet is spinning. And you are on the other side of the planet. It's going a few hundred m/s in the opposite direction. You will be quite supersonic. If you want to survive, you had better brought along a vehicle you can decelerate and land safely in (it could just be a box with a parachute). And have teleported high enough in the air to give you time to do it.
Say you teleported east a quarter of the way around the earth. Then on arrival you would be traveling up at a few hundred m/s. You will zoom upwards on arrival. No problem, but you better have a way to break your fall when you come back down. Or, just before you hit, teleport to the opposite side of the planet from where you started. :)
What if you went west instead? You would be going down. Really fast. If you come out at ground level, you become flat. And create a hole. Best again to come out high up in the air.

Teleporting east in little steps will just add a little jump to your walk. (How far east to get a half meter jump from each teleport?)

What happens when you go north/south?
Is there someplace on the planet you can arrive with no velocity difference?

Vinge pictures commerce by a network of lakes, stepped across the face of the planet, and covered wooden boats built strongly enough to handle the impacts of arrival.

[Back of my envelope... velocity]
How fast is the ground moving?
Earth radius is 6 × 10⁶ m, so circumference = this x 2 x 3, say around equator). And that much rotation takes a day, so 36 × 10⁶ m/day, 1.5 × 10⁶ m/hr, 4 × 10² m/s. ~400 m/s. At the equator - higher latitudes are slower (having smaller radii from the earth's axis).
(400 m/s ~= 1000 miles/hour).

History:
  1999.Apr.20  Identified Vinge book, thanks to a reader.
  1997.summer  Created.