Update: It looks like my ‘easy’ fix has not worked for many users. It looks like now like this is an Apple issue that they are aware of and working on. In the meantime, the best current workaround seems to be this one: Go to the Purchased section in the App Store, make sure you’re on the All tab, and scroll through and apply updates.
I’ve seen a large number of users saying that the App Store Updates page is not working over the last few days. I experienced the issue myself – with the App Store icon badge showing a number of updates available, but the Updates page was completely blank.
It looks like there is a very easy fix for this though – the old school, cure-all fix for computer issues of all sorts. Reboot the iPad. Just power the iPad off and back on like normal. Just to be clear, to reboot the iPad you hold down the top Power button until you see the ‘Slide to power off’ prompt, then slide to power off. Give it 10 seconds or so and then hold the power button down again until you see the Apple logo appear on the screen.
That simplest of solutions has worked for me. Let me know in the comments if it works for you or if you have another solution to the issue.