I shot this handheld with my iPhone 4s, so it's pretty shaky. I used the Warp Stabilizer in Premiere Pro CS6 with the default settings, and it's almost like magic! All the finishing was done inside of Premiere Pro.
This footage from Uganda (courtesy of the Forestry Extension Institute, skogkurs.no) was shot on an iPhone, and the colors drifted and changed a lot during the shots. Some clips also needed stabilizing. This is just a handful of clips, but the project had hundreds of clips like these that needed some work.
I did some training with their editor, and she was able to finish the film with a much better quality than they thought was possible. She used CS5.5, but I borrowed some of her material so I could try out the new tools in Premiere Pro CS6. CS6 speeded up the process considerably.
This video shows the film Making Tar (vimeo.com/40581474) before and after color grading and finishing in Adobe Premiere Pro. Primary and secondary color corrections, stabilizing, sharpening etc. all done in Premiere Pro CS6.
A before & after comparison, with and without color correction. The slo-mo is a result from recording at 50p and editing in 25p in Premiere Pro with 50 % speed - except the super-slow one at the end. That one is made in After Effects with Pixel Motion in Time Warp. All the color correction was made in Premiere Pro.
Some people recommend that Premiere Pro editors should transcode their 8-bit footage to 10-bit before grading. This is supposed to increase the robustness of the footage when grading heavily.
Since Premiere Pro works in 32-bit internally, this seems like an unnecessary extra step - and since every conversion/transcode operation will degrade the footage to some extent, it's more logical to use the original file for grading. So I did a test with heavy grading of a gradient sky using H.264 DSLR original footage and a copy transcoded to 10-bit ProRes 422.
Watch the results, and decide if you still want to transcode for grading purposes. There are many other reasons to transcode - this test only looks at image quality after grading.
This is of course an 8-bit exported H.264 file, but the differences were the same in Premiere (both on a 10-bit display and an 8-bit display) before export.