Can you post a pic -- a clear close-up -- of the black dots/spots?
The other symptoms you describe could be from letting it get too dry. Jades are succulents, but not desert cacti. Try watering it about every 7 days.
Also, when you water it, give it plenty, not just a sip.
If the Leaves start to wrinkle before 7 days go by, water it every 5 days. They don't like a lot of heat, so keep yours at average house temperatures.