Situation: some MongoDB documents have subdocuments that contain an empty key, e.g. (I stripped ObjectIDs to make the code look nicer):

{ 
    "_id" : ObjectId("..."), 
    "stats" : 
        { 
            "violations" : 0, 
            "cost" : 170, 
        }, 
    "parameters" : 
        { 
            "" : "../instances/comp/comp20.ectt", 
            "repetition" : 29, 
            "time" : 600000 
        }, 
    "batch" : ObjectId("..."), 
    "system" : "Linux 3.5.0-27-generic", 
    "host" : "host3", 
    "date_started" : ISODate("2013-05-14T16:46:46.788Z"), 
    "date_stopped" : ISODate("2013-05-14T16:56:48.483Z"), 
    "copy" : false
}

The problem is line:

"" : "../instances/comp/comp20.ectt"

it is impossible to get back the value of the field. Querying doesn't work:

db.experiments.find(

,

)

gets the full content of the parameters subdocument. (My guess is that "." is probably ignored if followed by an empty selector.) From the JSON specification (15.12.*) it looks like empty keys are allowed.
Moreover, renaming doesn't work either, for similar reasons.