Does anyone know of a PS script that will apply the image filename to a batch of images sort of like a watermark?

I don't know how to do this in Photoshop, but I could do it in Portraits and Prints.

You can do that through the File->Automate->Web Photo Gallery. Select "Security" under "Options" and change "Content" to "Filename." Then you can control where it goes.

Using this you can resize and add a watermark to a batch of images, say, for a web display.

If you specifically need a script to do this, send me a PM. I have one I wrote a long time ago you can probably modify, assuming you know JavaScript.