If there was something inherently wrong with the update that Apple needed, and could fix, then why is it that the Update has worked on other devices, iPads, iPhones etc..?
The Update is just a set of instructions. If you hand a sheet of Paper to 10 people with the exact same set of instructions, but 2 have issues with whatever the instructions had them do, then do you automatically assume the instructions have an error that needs fixing, or do you perhaps think that the 2 people with issues may have done something wrong, or something happened while they were following them?
Now I'm not saying you did something wrong, during the update, but It is possible that something happened during the update that caused a file to corrupt, or was improperly copied over etc... something that is out of Apple's control.
Because, with all things being equal, if you follow the same set of instructions the same way every time, the results should be the same. Since the update did not change between your iPad and someone else's, then there's other factors here to consider.
Again, if there's something inherently wrong, why is it My iPad works with the update? The error could not have magically corrected itself on my iPad but not yours?
The issue here, is not that Apple needs to fix a phantom problem with their update, its that something happened while updating, that is basically impossible to foresee, or account for.
As StarTraveler has said, many people have been able to resolve their issues by Resetting, Resetting all settings, or even Restoring the iPad to Factory Condition using a computer running iTunes.
If you have not done so, Its a good idea to try it. And even if you have done so, its a good idea to try it again without restoring a backup, if only to see if it runs o.k without anything on it to rule out possible culprits.
Ohh, and FYI, I own an iPad 2, almost 3 years old. Cracked screen, and non functional home button due to a drop, that works perfectly fine on iOS 8. Software wise everything works the way it did on iOS 7, and sometimes even better,