my american bulldog does that when she's really excited, or anticipating something... like in the boot when we are nearly at the beach etc, but seeing as you mention your dog is from rescue i would guess that is is stress related?
1 month. Bless him he's doing so well. I know it's early days but he always looks like he's done wrong? No one could toilet train him which I find odd, I've had 3 accidents that's it?
i would hazzard a guess that he is just a bit insecure given his start in life.
give him time to settle in and im sure he will soon grow in confidence. i would not pander to him or give him attention when shaking, as this will just re-enforce the shaking as he gains affection from doing it.
be patient and consistent- sounds like what he needs.
good luck with him, sound slike he has finally fallen on his feet.
Don't underestimate him just feeling cold! Mine will actually pull duvets over themselves when they get chilly. All of mine will shiver if they get cold...