I had a problem with my Home button before the update, but it worked better again afterwards.
If you're still on iOS 8.1: the latest software, which is 8.1.1, was released to improve the performance of the iPad 2.
Here's a fix that helped me with my Home button before the update:
Open one of the built in apps (Mail, Settings, ...). Press and hold the Power button until you see the slider to turn off your device. Then let go of the Power button, don't turn it off. Press and hold the Home button until the slider disappears and the app you had opened is closed, so you see the homescreen.
My Home button wasn't working perfectly afterwards, tbh, but I didn't have an unresponsive button as often as before.