I just had some work done on the rear differential (gear whine), and since then I've noticed this consant hum-like noise that starts after 20 mph or so. It kinda sounds like tire noise, but has a metallic quality to it. I know it's not tire noise because it doesn't change pitch with changing speed. That's also why I think its' not the differential or tranny.

So, I just noticed that since getting it back, the drivers' side tailpipe/muffler is lower then the other one and rotated a bit. They were even before I took it in. Is it possible that a poorly aligned tailpipe might induce drone and that's what I'm hearing? Do they even have to remove the tailpipe to do differential work?

 

There may be a leak at the clamp. From what you had discribed, I doubt that you're hearing "drone"... Who knows, maybe a baffle came loose inside the muffler. Try hitting it with a rubber mallet.

 

Rich- Check that over-axle clamp to see if it's loose. They should not rotate as you described.
Once you fix/verify that and if you still have that 'drone', you can move on to another suspect part.