I've been using Kingston 8gb SDHC cards just fine. I seem to recall the manual stating that 32gb was the limit.
edit-
The recorder does NOT appear to save the file if the plug is pulled while running on external power.
The PP-99 external li-ion battery seems to run the box just fine. I got almost 3 1/2 hrs on set of new AA Sanyo 2700mah's with their first and only charge so I imagine the PP-99, at 4000mah, to handle most of our situations just fine. However, I should note that the adapter tip that comes with the battery (that fits the 661) absolutely sucks. If you rotate it ~90deg the unit shuts off. I hacked and old PS with a tip that fits the 661 much better and joined it with the battery cable.