Re: My S4 will not recognize any SD card but my PC does.
And if you don't get their full cooperation, remind then that it's the law that says that they're responsible for what their update does. (There are different liability laws in every jurisdiction, but they all basically say "you broke it, it's your responsibility". And they can't escape it by putting something like "by accepting this update, you accept all responsibility", or something like that. They can make the claim, but the law doesn't accept it.)
Depending on your carrier, though, you'll get more or less cooperation. AT&T actually apologises when that happens. (I got "I'm so sorry, but we're going to have to replace your phone".) Usually they just reflash the update, because the way Android OTA updates is done is at least pre-1988 technology (because in 1988 I wrote a much better method of live updating - one that doesn't cause the update to actually happen if it fails; all that happens is that you're left with the old version and can try the update again).