Mongoexport -q ISODate query

mongoexport queries require the use of strict-mode MongoDB extended JSON. You can read more about that flavor of extended JSON in the MongoDB Manual article on extended JSON. In your specific case, the proper way to write the first query in the mongoexport command is

mongoexport.exe -h *MYHOST* -p *MYPORT* -q "{ 'time' : { '$gte' : { '$date' : '2014-12-21 12:57:00.506Z' },'$lt' : { '$date' : '2014-12-21 12:59:00.506Z' } } }"

I had the same problem with mongo 2.4, you need to use $date with "a 64-bit signed integer for milliseconds" (https://docs.mongodb.com/v2.4/reference/mongodb-extended-json/) in your case:

mongoexport.exe -h *MYHOST* -p *MYPORT* -q "{'time':{'$gte':{"$date": 1419166620506},'$lt': {"$date": 1419166740506}}"

I used @wdberkeley's answer as a starting point but that particular date string did not work for me. I had to use a 'T' to separate the date and the time:

mongoexport --username user --password pass --host host --db dbName --collection coll --type=csv --query '{"_created_at": { "$gte" : { "$date" : "2017-12-21T12:57:00.506Z" } }}'