DVDdoug:
First, you cannot connect a regular 8-Ohm speaker. It says you can connect headphones or Active (powered) speakers. That means something like computer speakers that have an amplifier built-in and plug-into wall power, or have "wall wart" power supply.That ground note is unusual... Normally a line-output is ground referenced. I didn't read the application notes so I don't know about the solutions or work-arounds. With headphones, it's no problem to have the ground "floating", but with powered speakers or an amplifier, etc., you'd have to deal with that ground problem.
P.S.
OK, I looked at section 3.2 of the application note. The solution is to add a capacitor to each output (C1 & C2 shown on the application note) and then use a real ground. This means you cannot use the 3.5mm headphone jack because it doesn't have a true ground. (You have to use "R" & "L", connections plus a ground pin.) You should be able to skip the other parts as long as you have the capacitors. 0.1uF capacitors should be fine.
Thanks for the help/direction.
I updated the OP with a link to an amp. Could you give a bit of guidance on how to hook up the amp to the mp3 shield. The grounding issue has me a bit confused. Thanks!