Adobe research scientist Wil Li has a demo of an experimental technology for creating seamless edits in interview footage that could make working with jump cuts easier. Hopefully, this technology with Content Aware seam-carving goodness will be integrated into Premiere.

Some of this seems to have been developed a little further and later presented as Tools for Placing Cuts and Transitions in Interview Video, SIGGRAPH 2012. Here's the video via John Nack:

If you'd like to see this in Creative Cloud (the feature hadn't made the cut by early 2014), you could make a feature request using the Adobe Feature Request/Bug Report Form!

Something similar is already in Avid Media Composer: the Fluid Morph transition, which was discussed by Genius DV earlier this year.

Perhaps tired of covering with cutaways, a few years ago, Wes Plate (now on the After Effects team) mentioned a tip he picked from an old Elastic Reality demo. In a blog post Goodbye Jump Cut, he discussed using the After Effects filter RE:Vision Effects RE:Flex (Motion Morph) to morph over jump cuts. Seamless smoothing over jump cuts can be quite complicated and may require animating and tracking masks of facial features (eyes as they blink, mouth, dimples, brow wrinkles, nostrils) as well as hair & clothing for the better part of a second on each side of an edit to guide the morph.

On the AE-List, Peter Litwinowicz and Jack Tunnicliffe added, and later Lori Freitag added a video demo (and another):

“This sort of morph can also be done using Freeform with the right size mesh to warp incoming and outgoing edit so they meet each other. … a key difference between RE:Flex and Freeform that I think would be really useful in this case would be our Auto-Align feature that will use optical flow to match up automatically all the extra bits after you align the major features by hand.”

If you don't have a 3rd party filter (or Fluid Morph in Avid), you're left with Reshape or Mesh Warp. It seems possible that AE's Timewarp filter could help (Premiere CS5 removed its Timewarp filter); see Motion estimated morphing time-remapping on stills. For more on morphing in After Effects, see the AEP round-up 2D morphing.