Images print oddly

If you have a lot of these pictures to scan, you might look at purchasing a decsreen plug-in for Photoshop. I've used one from Sattva which is pretty darn good, and maintains details in the shadows.

To expand on what James Gifford said, look in the scanning software to see if it has an option labeled something like “Halftone removal” or “Descreen”. The image below is what it looks like in the scanning software I use:

Basically, the print of the image has no actual gray shades because it was printed with fully black ink, so the only way to simulate gray shades was to render it with a halftone screen applied, which is a pattern of larger and smaller black dots. It’s that pattern that interferes with the pixel grid of a digital image and causes the moiré pattern.

This is a very common problem when scanning old images printed on a press, so if you do web research using terms like “descreen halftone scan” you’ll find a long list of techniques and plug-ins; some work better than others and it isn’t always possible to remove it completely. Whatever is used must match as closely as possible the frequency, angle, and dot shape of the halftone screen that was applied to the image when it was prepared for the press, and then undo that back into gray shades.

It looks as if you're getting moiré patterns from the interaction of the source's half-toning, the scan and ID's processing of the image.

I'd take your best scan, straighten and crop it in Photoshop, (optional: convert to Grayscale, or use the Black and White feature to do an optimized color conversion), adjust the tonal balance as best you can using Curves (keeping in mind it will always print a little darker than you see it on the screen), apply a very slight blur to blend the halftone dots (I've had a lot of success with a Median-blur-then-sharpen cycle, but you may have to go through a dozen iterations to find the optimal one)... and then scale it down to no more than 600ppi for your intended print size. 300ppi is probably more than enough. Try different scaling modes, but I'd say a blur mode will work best. You'll lose some detail but get a "better" illustration overall.

What you want to do is (1) remove the halftone screening as much as you can and (2) pre-scale the doc to something reasonable so that InDesign doesn't have to do all the heavy work.

If you're going to reproduce in color, I've found it best to work in grayscale, via a Black and White conversion, and then re-apply a sepia tint.