I dismissed ED-E while in the NCR CF after the raid and now cannot find it in Primm anywhere. I've looked in the shop multiple times and waited for days and days. I've been to the scrapyard, and the dialog options for the quest aren't there. Where has it gone off to?

This happened to me as well the first time I dismissed him. Luckily I am on a PC so I brought him back with the console and he went back to the shop if I dismiss him again like he should.

If you're on Xbox or PS3 you're screwed. If you're on PC the console commands are:
prid 1732D1
moveto player

I dismissed him and found him again in primm in the old man's shop right were you first found him. At least it did work for me.

What I found out, is that when you dismiss him, he travels back to Primm, but he walks all the way there! So the farther you are away the longer it will take him to get back. The only hope I have is that he doesn't enter combat in the meantime and possibly lose him forever!