I had a similar problem, and the whole experience was rather dramatic. I found that still photos would sometimes display properly, and sometimes not.
I imported photos to iMovie 10.1. I used three methods for importing photos: clicking on the "Photos Library" in the Libraries pane on the left side of the window, dragging and dropping from the finder directly to the Timeline, and using the "Import" window to identify and import still photos. I was importing JPEG, TIFF, GIF, and probably a few other file formats in my efforts to use still photos that would display properly. Sometimes I saw the photo for a moment, then a flash of bands of purple, green, and white, with patterns in the color bands. Some photos would display these color bands for the duration of their time in the video, and some would flash this pattern on and off. Some displayed properly. It didn't seem to matter which file format I used or where on my computer the photos came from or which import method I used. The problem occurred mostly with photos that were in the cutaway line of the Timeline (above the main video, but below titles, and it seemed to happen to photos that abutted other photos and had effects applied to them, like color correction and/or Ken Burns). The problem was persistent and seemingly random. I was, over the course of about five days, increasingly worried that I wouldn't be able to deliver the videos I was working on to my client on time.
First, I read everything I could find on these pages about this issue, and I tried all the suggestions I could that worked for other people. Nothing worked.
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I called Apple Care. Over the course of three days, I talked to four advisors. I tried a number of their suggestions, including:
Creating a new iMovie Library, like this:
File > Open Library > New ... > (Name the new library)
I also duplicated my project in the Projects window.
These things seemed to help a little, but the problem wasn't gone.
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Then I backed up my computer on Time Machine and uninstalled iMovie (moved it from the Applications folder into the Trash, no need to empty the Trash). I reinstalled iMovie from the "Purchased" window of the App Store. I had to quit the App Store and relaunch it to update it.
This seemed to help a little, but the problem wasn't gone.
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Finally, I resized all the still photos to be no more than 3000 pixels on the long dimensions and also no more than 2250 pixels on the short dimension. I was told by the Apple Care advisor that the Mac processes smaller photos differently from larger photos, and that these dimensions are how the computer differentiates smaller photos from larger photos.
It worked.
I made a few test videos. All the photos displayed properly, every time.
My next step would have been to reinstall the operating system, but I'm glad it never came to that. I was told that this is an issue Apple is investigating, and that I could expect it to be addressed in an iMovie update at some point. In the meantime, resizing photos appears to be the workaround I need to use now.
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FYI, I wasn't charged for my phone calls to Apple Care.
I'm using OS X El Capitan v.10.11.2 on a late-2011 MacBook Pro. I will also, in the future, be slower to update my operating system. I regretted installing the new version so soon after it was released. Had I known then what I know now, I would have stayed with Yosemite for six months or so before updating to El Capitan. I am also, as a result of this odyssey, buying a much larger external hard drive (4 TB) and trimming down the volume of data on my laptop, so that I can have more copies of Time Machine backups that the paltry 3 or 4 I now have on a small (500 GB) external hard drive. Reverting to an earlier Time Machine backup appears to be a solution to many problems.
May the force be with you.
Amanda