One approach to this is to use the str.search(regexp) function to find all parts of it that fulfill the JSON regex found here. So you could write a function that searches over the string for regexp matches.
To actually extract the object from the string you could use these two functions for the regex and then loop over the string until all objects have been found.
var match = str.match(regex);
var firstIndex = str.indexOf(match[0]);
var lastIndex = str.lastIndexOf(match[match.length-1]);
var JSONobjects = [];
while( str.match(regex){
//extract the wanted part.
jsonObject = substr(str.indexOf(match[0],str.lastIndexOf(match[match.length1-]));
//remove the already found json part from the string and continue
str.splice(str.indexOf(match[0],str.indexOf(match[0] + jsonObject.length());
//parse the JSON object and add it to an array.
JSONobjects.push(JSON.parse(jsonObject));
}