Holding RED as a shoulder-mounted rig should minimize most stability issues like the shakes and twitches you get with smaller camcorders. Kinda like others have said, the mass helps and most other broadcast cameras don't have much for stabilizing features. Some jumps and jitters can be corrected in post, but you usually have to crop in on the frame and it's hard to correct for those really quick motions that blur.
Anyway, I think that from an ENG/EFP perspective, the manual focus (incredibly innovative focus assist feature not withstanding), is going to be your biggest obstacle for run-n-gun situations. But if you can pull it off, you should have some of the finest looking news footage out there. :)