This happened on my 8700c which had a keyboard that didn't move at all previously. When I got another 8700c which had a non-moving keyboard I compared the two. There's a clear plastic piece that sits under the keys. There are a couple of points on that piece that hold it in place. One had broken on the older 8700c with the shifty keyboard.

I don't know if this issue is the problem with other models...

That would make a lot of sense in my case because the keyboard is shifty only on the right side. The left side is solid, as I would prefer it to be. The shiftyness doesn't necessarily add to the ease of typing. I'm still getting used to the 8703's full keyboard, though, after more than a year with 71xx models.

I still have some time left on Verizon's 14 day exchange policy. I'll probably switch it out for a new one.