Whenever attaching a screenshot in a Service Desk ticket though the Attachment option on the comment box on the bottom of the page, the attachment ends up on the case with a small thumbnail before actually attaching the full-sized thumbnail image. Please see the following screen shot to exemplify:
This ends up causing multiple messages on the customer portal side of things about an attachment being added on the case.
The only workaround is to actually remove either the small or the large thumbnail images. Even so, this will not stop any update notification from being triggered multiple times.