Date query with ISODate in mongodb doesn't seem to work

Although $date is a part of MongoDB Extended JSON and that's what you get as default with mongoexport I don't think you can really use it as a part of the query.

If try exact search with $date like below:

db.foo.find({dt: {"$date": "2012-01-01T15:00:00.000Z"}})

you'll get error:

error: { "$err" : "invalid operator: $date", "code" : 10068 }

Try this:

db.mycollection.find({
    "dt" : {"$gte": new Date("2013-10-01T00:00:00.000Z")}
})

or (following comments by @user3805045):

db.mycollection.find({
    "dt" : {"$gte": ISODate("2013-10-01T00:00:00.000Z")}
})

ISODate may be also required to compare dates without time (noted by @MattMolnar).

According to Data Types in the mongo Shell both should be equivalent:

The mongo shell provides various methods to return the date, either as a string or as a Date object:

• Date() method which returns the current date as a string.
• new Date() constructor which returns a Date object using the ISODate() wrapper.
• ISODate() constructor which returns a Date object using the ISODate() wrapper.

and using ISODate should still return a Date object.

{"$date": "ISO-8601 string"} can be used when strict JSON representation is required. One possible example is Hadoop connector.

From the MongoDB cookbook page comments:

"dt" : 
{
    "$gte" : ISODate("2014-07-02T00:00:00Z"), 
    "$lt" : ISODate("2014-07-03T00:00:00Z") 
}

This worked for me. In full context, the following command gets every record where the dt date field has a date on 2013-10-01 (YYYY-MM-DD) Zulu:

db.mycollection.find({ "dt" : { "$gte" : ISODate("2013-10-01T00:00:00Z"), "$lt" : ISODate("2013-10-02T00:00:00Z") }})

Try this:

{ "dt" : { "$gte" : ISODate("2013-10-01") } }