Is there any bug shooting utility submitting directly into Redmine? Something like bugshooting.com is doing with FogBugz.
Usersnap for Redmine is exactly what you need.
Add Usersnap to your web project and connect Usersnap with Redmine - you will get bug screenshots directly added to your Redmine tickets as attachment.
Full disclosure: I'm CTO and Co-Founder of Usersnap.