I just tried it out again. I'm afraid Gimp's interpolation algorithms don't seem to handle screen patterns as smoothly as Photoshop's.
The easiest way to deal with this problem is to not scale down from 600dpi/actual size.
The other option is to use a FFT Plugin (http://registry.gimp.org/node/19596) for Gimp to descreen before scaling down:
The video uses a different plugin, but it works in exactly the same way.
Here's a neat little trick I use to speed up the process: Instead of painting out all the "stars" (except for the one in the center - that one must stay intact) by hand I simply use the elliptical marquee tool to make a selection around the center star, invert the selection (selection->invert) and then apply a heavy gaussian blur. If the image has too many artefacts after applying inverse FFT, I undo everything and start from the beginning with a slightly bigger selection.
The good news is that your new scan is not suffering from blown out shadows and highlights like your last one did.
Don't be afraid to use the levels tool in Gimp. You've protected the shadows and highlights during the scan so now you have something to work with using a tool that lets you do a better job.
I'd certainly bring up the shadows a bit, setting the slider to where something is about to happen in the historgram:
In Photoshop, where I have better visual control over what I'm doing, I'd also clip the highlights so that the white scanner background gets blown out, but the whites in the cover don't. In Gimp I'd leave them alone, just to be safe.