If you didn't use relative file paths in your scripts, where possible, maybe you should have. Of course, in WED, you can use directories instead of a .wad file for textures you use with level geometry, and internally, the paths to those directories should be relative (hopefully).

I don't know what file path issues are specific to publishing, but when I simply move one project directory + all files and directories within that project directory to another machine, and then, execute (+ compile) the main script for the project, I rarely, if ever, have additional script errors or other errors. This might be because I try to keep everything related to the project, encapsulated in that project's directory. (Of course, this also has disadvantages.)

This is probably very obvious, but if you've used any "commercial" only features in your project when working with a "Team Commercial" edition, you might notice some changes when you execute the project with a "Standard" edition.