While most of us expect rotated or scaled pixel art art to look rather wonky and distorted, you usually consider translations to be "safe". But at least in 3.7.16 beta, there are some issues where images and image sequences, even when placed on the same bone, will judder and slide next to each other when translating in pixel grid mode.
To save everyone the trouble, this happens if the image files are not of EVEN dimensions and if the bones are not at integer positions.
Similarly, in Setup mode, the edge pixels of odd-dimension images can get clipped off. I didn't notice it in animate mode, which doesn't mean it won't happen.
So if you have a file that's 97 x 33, expand it to 98 x 34. If you are like me and reflexively crop everything to fit an animation, you might have a lot of files like this, so be careful.
Next, re-attach it to the bone fresh, since for some reason it "remembers" the old, bad offsets if you just let the app refresh itself.
To attach images "properly" for pixel grid animation, go into setup mode, and make sure that all bones are positioned at integer offsets (like 33,2 rather than 32.9, 2.3). Then make a dummy bone at 0,0 in world space and drag your images onto it. If it's a sequence you have to drag the first image by itself and then the others because otherwise it will create a separate slot for each image rather than putting them into the same slot. Without touching or adjusting the images by themselves, move the dummy bone until the images are lined up in the place you want. Set the dummy bone's position to an integer value, then drag the image slot onto the actual bone you want it on. In pixel grid mode it can appear like it's lined up perfectly but if you don't have your dummy at an integer offset, it the images will differ in offset from other images by a fractional amount, causing them to jump around as the parent bone animates.
I realize this is still just a beta but I wanted to make users (and the team) aware of the issue and how to work around it.