D.M. Procida wrote:

I have one of these:
http://www.habitat.co.uk/cleo-cd-storage/-//fcp-product/997898 that's
going to need to be wall-mounted. 400 CDs make quite a weight, and the
thing is heavy enough to begin with.

I have three radiators that are hung on plasterboard. I suspect there's
not much difference in weight between them and your CDs.

The fixings used were these:

http://www.amazon.co.uk/dp/B0001P0K9A/

Much depends on the thickness and quality of the plasterboard and how
many fixing points there are.