I thought I found something kind of cool: batch Shake Reduction using the Instant Movie feature. While Shake Reduction does an excellent job -- normally on one clip at a time -- there can be a lengthy wait before you can stabilize the next clip. I wanted to stabilize several clips without user intervention, while I watched TV.
All I did was put some clips on the timeline separated by 5 seconds of black video, then created an Instant Movie (Pan and Zoom theme) and opted out of all the options so that no edits were applied. After the instant movie was created, I applied Shake Reduction to the Instant Movie. When Shake Reduction was finished on the Instant Movie, I exported it to an MP4 file. All the clips within the instant movie looked beautiful. Then I saved the project, only to find out that the entire Instant Movie was corrupted when I opened the project later.
(I was more successful when I used Prodad Mercalli 2.0 to stabilize the Instant Movie. The saved project opened without the corruption. )
Two important points: Export your project to a suitable file format before you exit Premiere Elements or start a new project, because that's as far as you can go with batch shake reduction, and don't use clips that are badly shaken. The shake reduction will be lost once you exit Premiere Elements or start a new project. And if a clip is badly shaken, after the Instant Movie is stabilized, the Shake Reduction status message may tell you there is too much cropping and to fix the problem and try again.
This saves a lot of time for me and frees me up for longer periods.