I inspected my U-joints a few weeks ago and none of them have play, even hanging on them with an 18" pry bar they didn't seem to budge. While I was looking at the U-joints at the rear end, I noticed three little raised areas of metal in a triangular arrangement where I'd expect a balance weight to be. They almost look like tack welds. There is no weight back there, could this be what causes the intermittent odd shimmy when I take off?
Yes. You should get your drive shaft u joints replaced and the shaft balanced at a driveline specialty shop asap. Even though you couldn't detect any play in the u joints, I would replace them now judging from the corrosion I can see on your picture. This is not an expensive proposition.
Try to clear that rust and see if they are still there. If anything was welded, it is a long time since its separation because spots are rusty too.
