This is from the Apple support forums:
Regarding your question, it is very strange that you can download apps but then can't update them. Try these steps:
Do the four finger swipe up to reveal your multi task bar along the bottom. It will show all the apps that you have opened at one time or another. Long press one of these apps until they start to jiggle and red minus signs will appear above them all. Press all the minus signs, this will close them, not delete them. It's a good idea to do this regularly just to keep them all running smoothly, I do mine every night. Check and see if it is operating now. if not a restart is in order.
Restart: Press and hold the power off button, the one at the top right. You will see a slide appear to power off, slide this and the screen will go dark and a Whirly will appear. When the Whirly disappears your iPad is now off. Press the power button again until the Apple logo appears, this will take a few seconds and your iPad will start again. You should restart your iPad occasionally also as it will keep it running smoothly. Now see if it is operating. If not a reset is the next step.
Reset: Hold the power off button and the home button simultaneously, keep holding them in and you will see the power off slide appear and disappear, wait until you see the Apple logo appear before releasing the buttons. It will take a little longer for your iPad to start. This is a reset. Let us know if this fixes it. Good luck!!
Hope it helps you out...I have a 64GB wifi ipad3 as well, and just updated a bunch of apps without issues....Have you tried it connected via cable as opposed to wifi? That might do the trick too.