"(note in passing - this is a great new feature, but it would be really nice if it showed some indicator that something is happening after the drop... as it is, there's no indication anything is happening, you can carry on typing etc, then suddenly the image appears at the current cursor location. It's fine with tiny images, but with larger ones users will think it hasn't worked, so try to drag it in again, and in my testing on the demo site it has been possible to drag the same image in multiple times concurrently)."

I acknowledge it is definitely a "your mileage may vary" improvement that probably only works best with super fast upload speeds. We will improve it over time as we figure out how to improve it, but if it doesn't work well then we still have the dialog to upload images with progress. For CKeditor, while we currently use a custom plugin, they are planning native support fro dropping images in version 4.4 of CKeditor.
I assume we will still have to provide the upload service page but perhaps they will provide a way to indicate progress during the uploads.

"I've just upgraded a site to 2402, hoping that dragging and dropping images into the HTML editors will make things easier for some of my users, only to find it doesn't work for me.
I've tested in Chrome and IE11 on Windows 8.1. In the former, the cursor changes to +Copy in the drop zone and I end up with a duff hyperlink to a local file:///... in the editor at the drop location.
In IE11 the cursor changes to +Move and the image opens in the browser, taking me away from the editing page."

Those are default browser behaviors that indicate our plugin has not hooked into the drop event. If that behavior happens consistently then it is probably not configured correctly, if it happens sometimes but other times it works then it may be a "your mileage may vary" thing. Though even when we do manage to hook into the drop event, we aren't doing anything to show the drag icons that is just web browser functionality.

"Is there something I need to configure to make this work? Perhaps I'm suffering from old cached javascript, but I've tried every refresh technique possible."

View the source and make sure it is loading the version of the editor that shipped with this mojo release, ie ckeditor432. Also check your user.config for any other custom settings you may have related to CKeditor, like if you are not using our default config file then you are missing the plugin which is added from /ClientScript/ckeditor-mojoconfig.js 

"Incidentally I cannot drag an image into this post either, but I can drop one into an HTML feature on the demo site (using IE11)."

Right, you don't see an image toolbar in the forums either unless you are an admin and it is working correctly on the demo site.

Hope that helps,

Joe