I have a simple script where I want to move an NPC which the player is speaking to while the dialog window is open. However, when I use the SetPos function the NPC isn't repositioned until the dialog window is closed. Is there some other way to move the character?

Being in Dialog means that you are in Menu, which means the game is basically paused.

You can use MessageBoxes instead, and have the NPC walk around while they pop up. But the entire thing will be a scripted event, and not a part of the Dialog window.