Using Sparkfun's MP3 player shield with an Arduino Ethernet Pro - SPI problems

I can see that the default hardware SS pin is 10, which is the same pin as the ethernet chip select pin. Is that causing any conflicts?

The SS pin defines which slave (the Ethernet card or the MP3 player) is to respond to the SPI command. If you try having two devices listen and respond at the same time, of course that will cause conflicts.