No issues with filling the card completely until you can no longer take the next shot.
I usually empty the card to a portable device or end of day. I usually have more than 1 card so I usually swap out the card during a brief lull moment during the shoot.
The card that is pulled out of the camera goes into my Nexto eXtreme 2700 portable device which automatically transfers the data from the card, verifies the data and then erases the data from the card. Now, this card is good to go again.