Multiple use of the positional `$` operator to update nested arrays

In case you can execute your query from the MongoDB shell you can bypass this limitation by taking advantage of MongoDB cursor's forEach function (http://docs.mongodb.org/manual/reference/method/cursor.forEach/)

Here is an example with 3 nested arrays:

var collectionNameCursor = db.collection_name.find({...});

collectionNameCursor.forEach(function(collectionDocument) {
    var firstArray = collectionDocument.firstArray;
    for(var i = 0; i < firstArray.length; i++) {
        var secondArray = firstArray[i].secondArray;
        for(var j = 0; j < secondArray.length; j++) {
            var thirdArray = secondArray[j].thirdArray;
            for(var k = 0; k < thirdArray.length; k++) {
                //... do some logic here with thirdArray's elements
                db.collection_name.save(collectionDocument);
            }
        }
    }
});

Note that this is more of a one time solution then a production code but it's going to do the job if you have to write a fix-up script.

The positional operator only supports one level deep and only the first matching element.

There is a JIRA trackable for the sort of behaviour you want here: https://jira.mongodb.org/browse/SERVER-831

I am unsure if it will allow for more than one match but I believe it will due to the dynamics of how it will need to work.