The rfid reader (MFRC522) does not work with the latest release of Jessie(2016-05-10). It works fine on the previous version (2016-03-18). I believe this is due to the new version of SPI.

On previous Jessie version (2016-03-18-raspbian-jessie) if I type lsmod after installing spi I get the following..
spi_bcm2708

On recent Jessie version (2016-05-10-raspbian-jessie) if I type lsmod after installing spi I get the following..
spi_bcm2835

Others, are having the same issue as described on the raspberry pi forum at this link..
https://www.raspberrypi.org/forums/viewtopic.php?f=107&t=148890