Despite being careful, I lost one screw that seemingly disappeared as I tried to place it back. Even a rare earth magnet didn't find it. It would be nice to have spare screws.
My replacement battery came with the ribbon cable facing the wrong direction. I had to fold the black part over so the connector was oriented properly.
I found that the black tape was like a bag--as I pulled it off, it filled with air, and the air did not escape when I put it back. I used the knife to make a small hole to let the trapped air escape.
The buttons will NOT "fall in" when reassembling, so it's important to remember to put them back. I found that putting them in the frame before replacing it is the only way. Check to see how they fit on the phone first, then drop them into their slots outside-in. The power button will fit only one way; the volume buttons should go in oriented as they fit best on the phone. Be sure to test them to make sure they click freely often! It's easier to readjust them before all those screws are back in.
The two plastic covers do not fit snugly in place, so after putting them back in place, use small bits of electrical tape to secure them before installing a new adhesive back cover. I tested my phone thoroughly before the last step, so that I would not have to buy a new cover if something didn't work.
My phone (purchased 12/2015) has only 2 silver screws top and bottom (4 total), and they're also T3, not Philips.
With a Torx screw this tiny, it pays to take time to make sure that the driver is well seated before turning it. This will eliminate stripped screws. Also, I loosened each screw first, and then removed them. Breaking them free before turning them also helps prevent stripping.