Microwave starts working when door opens - how dangerous is it?
It is dangerous to humans because it heats up things that contain water. 
You contain water. Some parts of you can't deal with this added heat (your eyes) and will be damaged first.

It also fries sensitive electronics like the embedded radio chips in your phone and laptop when they are close enough. (meters away, not centimeters)

Also, there are laws for for the amount of leakage of a microwave, and being on with open door certainly violates this law. Please unplug and don't use it, ask the landlord to replace it.