Drop shadow in Adobe Illustrator not working properly

I've been able to reproduce this. I opened the same circle test on both my Mac and a Win PC, and the Win PC showed signs of the same stair-stepping (left), where the Mac one was not affected (right)

That being said, this seems to be just a screen display anomaly. The output of the file is not affected. e.g. if you export it as a PNG, it's fine.

Thanks everyone for your help.

I think it is a kind of glitch going outside the norm. I have found a work-around. But also think I might have created the problem.

So prior to the problem about a week ago, I read somewhere that you can create larger than the max artboard size which is a about 5200mm. 

So I created a 10meter artboard from the new document panel. So now I find that on large created artboard the shadow is fine. But if I copy and paste the same item into the smaller artboard the lines appear in the shadows.

Left image on 3000mm artboard.  Right image on 7000mm artboard.

I can see the problem, changing the raster effects resolution did not make a difference.

It may be caused by the large size of your dropshadow and a limit in Illustrator.

You could try if creating the blurred shadow object in Photoshop works better?

That can happen with super large objects.

If you draw a black shape and then apply the Gaussian blur effect - does that work?

Go to Effect - > Document Raster effect settings , Change the resolution to 300 

My first guess is the drop shadow effect is actually being applied to more than one object. Seams like that should only occur at object edges. What does the artwork look like in outline view? The Appearance panel could provide some clues. Isolating the affected object on another layer might make it easier to organize any of the elements involved and eliminate certain elements that could be causing the problem. If the artwork was made by someone else and/or imported from a PDF there could be clipping masks, clipping groups or other stuff that wasn't readily visible. Isolating the element on a different layer can make it easier to release any of that stuff, examine what's listed in the object tree (in the Layers panel) and get rid of the unnecessary stuff.

If the artwork was imported from a PDF all sorts of "trash" might have been included. That might mean duplicate paths that are not painted or stroked, basically invisible. Sometimes imported PDF-based artwork might include rasterized (pixel-based) elements that have been sliced into strips or even tiles. Plugins like Vector First Aid can automatically clean up a bunch of that stuff. Otherwise it has to be cleaned up manually. When it comes to drop shadow effects in Illustrator it is best to have those applied to only one single path, not a group of objects.

I could not duplicate the problem that you are having. Is this happening in just the one file or in any file that you try to apply the shadow effect? Can you show the entire file so that there is more context to what is going on? Could you give specifics as to how you made the drop shadow? What version of Illustrator and what operating system are you using?