I too am having problems with the Due and WiFi shield. Running R3 WiFi and the WiFi example.
Problem 1: Running Examples/WifiWebServer (modified only for my ssid and pw): I have to press reset on the Due multiple times before it gets past "WiFi shield not present"
Problem 2: As in 1 above the server stops responding to port 80 connection requests after a few seconds, although the first few connections/requests work fine.
Problem 3: A jumper between pin 3 and 7 prevents the WiFi card from doing anything.