1- The car: When Iron Man comes cracking down to Earth in Tennessee he barely missed a car WHICH GOES CRASHING OFF THE ROAD. Uhm - A car crash like that would have caused a police report and of course news media around a flying metal man falling from the sky. Yet - no mention of it after we see the car crash off the road.
2- The kid: When the kid first sees Tony Stark he informs him that he's dead according to the news paper that identifies him on the cover. Yet - 5 minutes later the kid asks Tony for his name and Tony says "The Mechanic." But the kid knew who he was because again, he identified him from the cover of the news paper. HUGE - plot hole/continuity error.
3- The hand cuffs: At the bar, the agent hand cuffs Tony behind his back. When Tony is outside the handcuffs are behind his back. Yet - magically - when Tony jumps through the glass window and then lands, the handcuffs are mysteriously now in front of him. And he fights the agent with the hand cuffs in front of him. HUGE - continuity error.
4- the hidden wrist blaster: Tony fights the first agent and never once uses the wrist blaster, not once the whole time, even though his life is at risk. Then outside he's about to die and we learn he has a hidden wrist blaster the whole time. Uhm - why didn't he use that on the first one?
5- the walkie talkie: When on the boat, Tony calls the Vice President on the phone. Yet when James Rhodes is shown talking to him on the phone, James is talking into the boats walkie talkie.