Continuity mistake: When the first Spider-Man is thrown into the car and bus, he uses the street lamp that's hanging over the middle of the bus to lift the car up with his webs; however, in the previous shot, the street lamp is near the rear of the bus and isn't really close enough to be hanging over it. It completely changes position to fit the action.
Continuity mistake: From the flagpole, Spider-Man pins 2 goblin soldiers to the building and his web covers their torsos, including their shoulders and all the way up to under their chins. When it cuts to the close up, they're still stuck to the wall, but there's no web at all seen, even though we see their shoulders, necks, and chests.
Chosen answer: He simply survived the crash without much explanation of exactly how. However, he hid from everyone after the crash to find out his truth, so everyone just thought he died. (This is common is comics where someone is presumed dead or in a situation "no one could survive" and then later shows up alive and the how isn't explained).