Maybe one of these suggestions will work. Ignore any that you have already tried.
Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons.
Make sure that you do not have a stalled download in iTunes - a song or podcast .... if you have a download in there that did not finish, complete that one first. Only one thing can download at a time on the iPad so that could be what is causing the problem.
If that doesn't work - sign out of your account, restart the iPad and then sign in again.
Settings>iTunes & App Store>Apple ID. Tap your ID and sign out. Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
Go back to Settings>iTunes & App Store>Sign in and then try to update again. Tap one waiting icon only if necessary to start the download stream.
You can also try deleting the waiting icons - tap and hold down on an icon until it wiggles - the tap the X on the icon to delete it. Then try to download again.
You can try resetting all settings. Settings>General>Reset>Reset All Settings. You will have to enter all of your device settings again.... All of the settings in the settings app will have to be re-entered.
If all else fails, download the updates or the apps in iTunes on your computer and then sync the content to your iPad.
Ios7 was clearly not ready for prime time, it saddens me that there are so many problems, and no clear benefit from the new ios. My camera will no longer function well, all apps greyed out and no solution ( according to the hundreds of frustrated posters here with same issue on multiple threads) I have always been an Apple devotee but this ios7 is a hellish experience, breaking all our devices. Why didn't they test it prior to release???????