I would like to use Gimp - or any other package running under Linux - to convert an image (colour or grayscale) to a series of binary dots, in the same way that newspaper pictures are printed.

If I convert the image to binary (line art) I just end up with a horrible mess.

I want to do this so that I can transfer to photo-sensitised PCB stock and turn the image out as an etching which can be used for making prints.

I don't know if this helps, but newspapers (and anything printed on a real press)
are done by halftoning. I believe this is more a function that's done when it's sent
to the printer, either printed directly, or outputing film, or direct plate imaging -
rather than when the image is converted. For instance, if I print a tiff image to a
desktop inkjet printer, I'll get sprayed color; but if I print the same image through
a rip to a digital duplicator, for instance, I can get those dots.

This might not help, but might push you in the right direction. There is another
open source app called Scribus that is becoming a DTP app. It might help, and
the mailing list has some folks in the printing industry who can probably answer
your questions.

Hope this hasn't just been useless rambling where you're concerned.

Hmm. That at least tells me what I'm actually trying to achieve!

So, I'm trying to reproduce what is normally a hardware-created effect. What I need, therefore, is some sort of "filter" to do that for me.

Thanks for that - it's got what I need to do clearer in my mind even if I still don't know how to do it!