I discovered this trick independently about a decade ago, to use cross-eyed viewing to easily spot differences between two similar images. Like you said, the parts that mismatch appear to shimmer and be unstable, making them obvious.

However, I feel eye strain from doing it, so I prefer other methods. 99% of the time, I do https://en.wikipedia.org/wiki/Blink_comparator instead, just switching between two images with zero flicker and zero displacement offset. Also with both eyes, it's easier to spot certain kinds of subtle differences like color shifts, JPEG-like compression artifacts, tiny differences in antialiased renderings, etc.

One benefit of the cross-eyed method, though, is that you can difference videos. But the use case for that is rarer than differencing images.