Use a zoom lens. Not only does it save you time and energy, but one of the downfalls of using mobile phones as movie cameras is the lack of a stable zoom mechanism. dSLR grips allow for much more stability, though.. we'll say only to an extent.
Add real hardware stabilization. Despite the better grip, dSLRs were made originally for photos - not film. Adding a counter-weight or stabilizer to the bottom of your camera reduces shake to near-zero and gives you smooth panning. You can DIY yourself or grab one of Glyde's camera stabilizers or Merlin's steadycam solutions (this one is slightly more affordable).
Use the right software. Although some may shun on "consumer" software packages, we've found Windows Movie Maker and iMovie to be just fine when arranging pieces together. But because of the simplicity of these packages, getting any of those "cool" movie-like effects is somewhat limiting. If you're up for the challenge, we suggest giving Final Cut Pro a shot to to step up your post-production game (given you can afford it, of course).
Are you a professional movie maker? We're just a few geeks who love to push the boundary of the gadgets we own, so any tips are more than welcome!