It might be little late(it is for sure) but posting it for future readers

You can use JSONObject optJSONObject (String name) which will not throw any exception and

Returns the value mapped by name if it exists and is a JSONObject, or null otherwise.

so you can do

JSONObject obj = null;
if( (obj = result.optJSONObject("ERROR"))!=null ){
      // it's an error , now you can fetch the error object values from obj
}

or if you just want to test nullity without fetching the value then

if( result.optJSONObject("ERROR")!=null ){
    // error object found 
}

There is whole family of opt functions which either return null or you can also use the overloaded version to make them return any pre-defined values. e.g

String optString (String name, String fallback)

Returns the value mapped by name if it exists, coercing it if necessary, or fallback if no such mapping exists.

where coercing mean, it will try to convert the value into String type

A modified version of the @TheMonkeyMan answer to eliminate redundant look-ups

public void processResult(JSONObject result) {
    JSONObject obj = null;
    if( (obj = result.optJSONObject("ERROR"))!=null ){
       //^^^^ either assign null or jsonobject to obj
      //  if not null then  found error object  , execute if body                              
        String error_detail = obj.optString("DESCRIPTION","Something went wrong");
        //either show error message from server or default string as "Something went wrong"
        finish(); // kill the current activity 
    }
    else if( (obj = result.optJSONObject("STATISTICS"))!=null ){
        String stats = obj.optString("Production Stats");
        //Do something
    }
    else
    {
        throw new Exception("Could not parse JSON Object!");
    }
}

I am using org.json.JSONObject. This is an example that you can use to test a JSONObject is null or not.

package general;

import java.util.ArrayList;
import java.util.List;

import org.json.JSONArray;
import org.json.JSONObject;

public class CheckNullInJSONObject {

    public static void main(String[] args) {
        JSONObject json = new JSONObject("{results : [{response:null}, {type:ABC}], error:null}");
        JSONArray array = json.getJSONArray("results");
        try {
          for(int i = 0 ; i < array.length() ; i++){
            JSONObject response = array.getJSONObject(i);
            if (response.isNull("response")){
                throw new Exception("Null value found");
            }
          }
        }catch (Exception e) {
          e.printStackTrace();
        }
    }
}

if(jsonObject.isNull("parentId")){
    jsonObject.put("parentId", 0);
}

http://msdn.microsoft.com/en-us/library/ms173224.aspx

The ?? operator is called the null-coalescing operator. It returns the left-hand operand if the operand is not null; otherwise it returns the right hand operand.

It is a JSON-B design deficiency. They could have done something slick like:

Json.createObjectBuilder().addIfNotNull("address", this.getAddress());

Json.createObjectBuilder().add("address", this.getAddress(), defaultOnNull);

I guess json passes null values as strings, so you can't check null as a java element. Instead treat the null value as a string as check this way:

if(!mapItem.getString("date").equals("null")) {
    //Value is not null
}

I have updated the code snippet in the original question to a working version.