When I open a chest, I notice that the lid goes up, but at the same time, the chest looks closed, albeit with a lid sticking out of it. I did have chests stacked on each other when I observed this, and it was a double chest, backed against a wall. I played around a bit, and found that when breaking a double chest, the breaking pattern appears on both halves of the chest, although only the half you are mining breaks. And if it's a stacked double chest, a strange graphical remnant of the half you broke will remain, and when you break the other half, there will be a ghost image of a double chest where the one you broke was. I fiddled around a bit, and couldn't reproduce the bug at all, so I took some pictures, and attached them. Hope you can figure out what's happening.
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I also realized (just after submitting this...) it may have to do with there being both a wall behind the chests, three stacked chests as shown, and a ceiling above the chests. So I fiddled with that, and didn't get very far, except to note that a fourth stacked chest seemed unaffected by all except the glitch where the breaking pattern appears on both chests. this I could reproduce on any double chest I broke. It could also have to do with directions on the compass, so note that these chests are facing south, towards positive z.