Verizon wouldn't replace my phone because they said there was physical damage near the charging port. Instead they made me go through my insurance with a $100 deductible and I'm obviously not getting the phone until tomorrow. Just stay away from this update - it's not worth the aggravation!
At this point, I realize this doesn't help you, but this is why I always call the CS 1-800 number vs. taking my phone to the store in person. Generally if you call and explain what happened as it did to you, they'll ship you out a replacement unit ASAP. Yes, you'll have to ship yours back for inspection, but personal experience tells me that "they" (whomever it is that receives the return) is MUCH more forgiving than the folks working at the stores. Obviously, if damage is significant enough it doesn't matter, but if we're talking about minor dings and dents here, let's face it, that's probably not what caused your update to fail.
I advised my sister to do this her S3 a few months ago. She had been using it in her armband while running, and condensation formed underneath the screen making it unusable. The water damage indicators were fine. I told her that if she took it to the store, they'd probably take one look it and refuse to believe it was a defect and wouldn't replace it. She called the 800 number, the CS rep was very nice and admitted that some screens did have an issue with condensation and agreed to send her a replacement right away. The rep did tell her that if it was determined to be caused by "user damage" when she sent it back they would charge her, but as long as the phone was otherwise in good shape and the water indicators were OK that it most likely would not be a problem...my sister received her replacement a day later and was never charged after she sent hers back.
EDIT: I just wanted to add that I'm not suggesting that calling the 800 number to go though Verizon's national CS is guaranteed to get you a new phone or is guaranteed to get you better service than by taking it to a store...I'm just sharing my personal experience. Your experience may vary. Obviously when dealing with CS reps on the phone, politeness is key...most will be willing to help as much as they can if you're pleasant to talk to.