If the Jenkins instance isn't deployed to the TOP level structure, plug-in doesn't recognize that and generates the wrong URLs which return HTTP code 404.

Example:
Jenkins is available at http://<host>/<dir>/ and so your 25th build of job A is http://<host>/dir/job/A/25/. Each build archives file TMP.txt.

A generated URLs for the artifact diff of TMP.txt is http://<host>/job/A/25/artifact-diff/24/TMP.txt?output=html

Fixed URL by hand: http://<host>/<dir>/job/A/25/artifact-diff/24/TMP.txt?output=html works.

The <dir> part of URL is missed in generated URLs.