It is possible to infer dates using a format of your choosing (I used the Date.toJSON format) with a little modification and also have reasonable performance.
Get the latest maintenance branch:
git clone https://github.com/apache/spark.git
cd spark
git checkout branch-1.4
Replace the following block in InferSchema:
  case VALUE_STRING if parser.getTextLength < 1 =>
    // Zero length strings and nulls have special handling to deal
    // with JSON generators that do not distinguish between the two.
    // To accurately infer types for empty strings that are really
    // meant to represent nulls we assume that the two are isomorphic
    // but will defer treating null fields as strings until all the
    // record fields' types have been combined.
    NullType
  case VALUE_STRING => StringType
with the following code:
  case VALUE_STRING =>
    val len = parser.getTextLength
    if (len < 1) {
      NullType
    } else if (len == 24) {
      // try to match dates of the form "1968-01-01T12:34:56.789Z"
      // for performance, only try parsing if text is 24 chars long and ends with a Z
      val chars = parser.getTextCharacters
      val offset = parser.getTextOffset
      if (chars(offset + len - 1) == 'Z') {
        try {
          org.apache.spark.sql.catalyst.util.
            DateUtils.stringToTime(new String(chars, offset, len))
          TimestampType
        } catch {
          case e: Exception => StringType
        }
      } else {
        StringType
      }
    } else {
      StringType
    }
Build Spark according to your setup.  I used:
mvn -Pyarn -Phadoop-2.6 -Dhadoop.version=2.6.0 -DskipTests=true clean install
To test, create a file named datedPeople.json at the top level which contains the following data:
{"name":"Andy", "birthdate": "2012-04-23T18:25:43.511Z"}
{"name":"Bob"}
{"name":"This has 24 characters!!", "birthdate": "1988-11-24T11:21:13.121Z"}
{"name":"Dolla Dolla BillZZZZZZZZ", "birthdate": "1968-01-01T12:34:56.789Z"}
Read in the file.  Make sure that you set the conf option before using sqlContext at all, or it won't work.  Dates!
.\bin\spark-shell.cmd
scala> sqlContext.setConf("spark.sql.json.useJacksonStreamingAPI", "true")
scala> val datedPeople = sqlContext.read.json("datedPeople.json")
datedPeople: org.apache.spark.sql.DataFrame = [birthdate: timestamp, name: string]
scala> datedPeople.foreach(println)
[2012-04-23 13:25:43.511,Andy]
[1968-01-01 06:34:56.789,Dolla Dolla BillZZZZZZZZ]
[null,Bob]
[1988-11-24 05:21:13.121,This has 24 characters!!]