My iPad 2 has become slow and unreliable progressively since iOS8. All part of the plot to persuade me to buy the new 9.7" iPad Pro no doubt. I just might succumb!
For what it's worth, my iPhone 4S had downloaded the faulty update but would not install it - it failed verification, telling me I was not connected to the internet even though I was. I have just connected it to iTunes which told me it was up-to-date with 9.2.1! However, doing the update on the phone worked as it usually does - I did not delete the previously downloaded version, the phone must have done that itself as Settings shows I have the latest build.
Just updated an iPad 2 and there seems to be an improvement in speed. At first the 'picture' was larger than the screen and I was afraid all was wrong but since a restart all has been well.