The problem-reporting thingie doesn't recognize me or my password. Do you have to have a separate account for that?

So I model a simple disc. Bring up the library, select an image, drag it onto the model, click "decal." I get an exception 001 message.

I'm using V15. V13 works fine.

Yeah, A:M Reports requires a separate signin. You can use the same user/password as the forums (I do just for simplicity) but you have to sign up for an account.

We are missing some important information here.

One of the great things about A:M is that you can often use a different method to accomplish the same task.
In this case you might eliminate the Library altogether to see if that that addresses the problem.
Open the image (or any image) in A:M and see if you can't get the image to apply that way.
If the image does apply then you know its not the image.
If the image doesn't apply then it may be your image.

Its hard to see what you are seeing so where possible post a screen capture of your desktop.
You might be surprised what will be revealed.

A:M Reports is great for its intended purpose but we first must eliminate user error.
If the image or shortcut in your Library is the problem that'll be easy to deal with.
The fact that v13 works while v15 doesn't is an important hint.

I take it this is happening with any image?

If this occurs with every image then you may have a corrupt IO file.
These files are located in your 'ImageIOS' folder.
On a PC these are usually located at: C:\Program Files\Hash Inc\v15e.0\ImageIOS

One thing to check with any image related disconnects is whether A:M knows where the image filters are.
You can find where A:M thinks they are via TOOLS | OPTIONS on the Folder tab (see attached image).

what is the image? Does this happen with all images or just the one?

Try importing it into the Images folder and drag from there.