Dito. Cut the wires and spliced with the new battery wires. Had to peal away some of the white tape on the new battery to get enough wire to work with. Used some of the kapton tape from the old battery to insulate the splices (electrical tape too thick).
Agree with Bill, I did break off one of the screw attachments. In retrospect, using a small putty knife between the cover and battery (which I'm replacing anyways) to apply force against the cover while prying at the hole would have helped.
Take heed to the note about getting the spudger between the dock connector and the cover. The dock connector is black plastic, as is the antenna cover, so it's difficult to see any gap between them. Putting the spudger between the metal shielding of the connector and the plastic is incorrect.
Stamp tweezers worked great for the ribbon cable! (Search eBay or Amazon, or your local hobby store.) This would be a useful tool for iFixIt to add to their inventory.
Same here, needed a heat gun. P.S. Harbor Freight had them on sale cheap (tip, not advertisement).
Prying with plastic spudger at the lower edge of the display housing bent the aluminum frame for me. Suggestion: if you don't plan on keeping the old glass, pry it away from the aluminum slowly (opposite direction than shown in step 33).