Not sure if this is related at all, but I also own the TF700 and I can't even see my SD card files in BSPlayer. I posted about it here:
BS Player on Galaxy Tab 2 (posted on the Galaxy Tab thread because it was the same issue I was having).
The SD card seems to be fine, because I can see its files in the file manager app. I have a 32gb SanDisk card (class 4), and unlike your card, movies seem to play okay once I can browse for them elsewhere. I just wonder if there is some compatibility issue with Asus that is causing various problems with sd cards.
Hope your new card works for you!