I have understood your problem. The whole string is actually a JSON object, where quote(") is present in the form of " ;.
First replace & quote; it with ". Then evaluate the expression and get the value of any item you want.
Below working code :)
<script type="text/javaScript">
var str1="{"actor":"100003221104984","target_fbid":"286108458103936","target_profile_id":"100003221104984","type_id":"17","source":"1","assoc_obj_id":"","source_app_id":"2305272732","extra_story_params":[],"content_ti":{"actor":"100003221104984","target_fbid":"286108458103936","target_profile_id":"100003221104984","type_id":"17","source":"1","assoc_obj_id":"","source_app_id":"2305272732","extra_story_params":[],"content_timestamp":"1325711938","check_hash":"892251599922cc58"}}";
var ans=str1.split(""").join("\"");
var obj=eval("(" + ans+ ')');
alert(obj.target_profile_id);
</script>
And see how your actual Data looks like:
{
"actor": "100003221104984",
"target_fbid": "286108458103936",
"target_profile_id": "100003221104984",
"type_id": "17",
"source": "1",
"assoc_obj_id": "",
"source_app_id": "2305272732",
"extra_story_params": [],
"content_ti": {
"actor": "100003221104984",
"target_fbid": "286108458103936",
"target_profile_id": "100003221104984",
"type_id": "17",
"source": "1",
"assoc_obj_id": "",
"source_app_id": "2305272732",
"extra_story_params": [],
"content_timestamp": "1325711938",
"check_hash": "892251599922cc58"
}
}