Is a Microwave oven without a faraday cage a health hazard? Microwave ovens have something of a Faraday-cage/shield to keep from leaking (emitting) EM radiation.
What would happen if the shield or the door was removed? No doubt it would be less efficient as an oven, and probably interfere with 2.4 GHz wireless technologies and such, but to what extent? 
Would it be dangerous/a health hazard? And with what kind of range? For instance, would you be able to sit in front of it? Would it disrupt WiFi and cell phone reception for the whole house or the whole block?
I'm told that 1W is the local legal limit for consumer-class wireless transmitters in my area, and that a 1W network interface controller is sufficient for establishing long range (<10km) point-to-point wireless links. By comparison, domestic microwave ovens supposedly output somewhere in the ballpark around 1,000W (e.g., the one in my kitchen is rated @ 1,200W).
 A: 
What would happen if the shield or the door was removed?

The microwave oven would not work. The door is provided with interlock switches. They prevent the oven from operating with the door opened. So the same would be true if the door is removed. If both of the interlocks fails (or are defeated), I believe ovens are also provided with a back up system, often in the form of a crowbar circuit that completely shuts down the oven requiring a service call. 
I should add that my knowledge is based on requirements that I was familiar years ago. Those requirements may have change. Best to check the current FDA regulations.

Would it be dangerous/a health hazard?

If somehow it were possible to operate the oven without the door in place, persons would be exposed to microwave radiation exceeding the US federal requirements for microwave leakage from a properly functioning oven, which I believe is currently max 1 $\frac{mw}{cm^2}$ for a new oven, and max 5 $\frac{mw}{cm^2}$ over the life of the oven. The primary health hazard, based on current mainstream knowledge, is injury due to the heating of tissue. Incidentally, in the early days of microwave ovens, specifically those used in commercial establishments, there was a worker or workers who deliberately defeated the door interlock system so that the door could be opened and closed without restarting the oven each time, thereby saving time. Reports were that the person or persons found that they gradually lost the use of the arm they used to place and retrieve food from the oven, due to cumulative thermal damage over time.

And with what kind of range?

The hazard diminishes with distance, since the  EMR intensity falls with distance. How much and how fast I don't know.

For instance, would you be able to sit in front of it?

Certainly not. 

Would it disrupt WiFi and cell phone reception for the whole house or
  the whole block?

Don't know.

I'm told that 1W is the local legal limit for consumer-class wireless
  transmitters in my area,

I'm not familiar with that limit. 
Hope this helps.
