I'm working through the G.E.C.K. Vault 74 tutorial and I have set up the two doors to teleport to each other, but when I load up the game with the Vault 74.esp selected in the launcher the door in the wasteland doesn't show up at all.

Are you sure you put it in the Wasteland world space?
And in a place that is actually accessable in the wasteland?

Some places are not accessable in the wasteland worldspace so it appears that its not working.
More information on what and where would help.

I used a manhole cover and placed it on the road just outside of Vault 101. I used F to drop it down to be level with the road.

It sounds like you did it well enough.

When you stand where it should be and point downward, do you see any "activate" option?

if not, maybe somehow your .esp isn't loaded or the contents didnt save. hmm.

If so, the door is actually a bit under the visible ground and you need to lift it upward a bit with the geck (hold down Z and drag the door, itll go straight up).

I've tried moving it and its still not showing up at all.

Try dropping some walls or big rocks into the area and see if you can see them? If you can't, all I can think is that you're not loading the .esp or, you're standing in the wrong place in the wasteland to see it. I've not had trouble with this part before.

What is your game version patched to?
What is you GECK version patched to?

They must be patched correctly to the correct level or the mod will be ignored in-game.

G.E.C.K. is 1.5.0.19 and Fallout is 1.7.0.3

Upload the ESP somewhere so we can take a look at it.

http://www.fallout3nexus.com/downloads/file.php?id=14801

That .esp has no door placed in the wasteland. The only records FO3edit sees are for that interior cell.

Your plugin has several errors with duplicate records. And the Vault 74 cell has no door connecting it to the wasteland.
Perhaps you uploaded the wrong plugin.

I've got it working. I had two Vault 74's and I didn't know it. I first started using the G.E.C.K. and I couldn't find my files. I then learned that I had to use it as an administrator. So I made it all over again and it turns out I was loading the old one. Thanks to all of you for your help.