According to Tony, the suits are coded only to him (with the exception of War Machine/Iron Patriot), however Pepper is able to operate the last prototype when it first comes on to her. Though this could be explained by a malfunction in the suit, near the end of the movie she is able to fire one of the arm/wrist components from another Iron Man suit.
When Igor (the big armor) is shown for the first time in the movie, the suit heads over to one of the crane's legs and stays under it to keep it from falling down but the crane doesn't fall down after all the suits have self destructed.
When Tony walks into the bar in Tennessee, there's a long shot of the sheriff sitting at the bar. In this shot, he is wearing a revolver on his belt, but later when Brandt takes his gun, it becomes a semi-automatic.
When Tony Stark first discovers the explosion in Rose Hill, TN, the map he views shows the town in extreme northwest Tennessee. However, later in the movie, the Miss Chattanooga pageant is taking place in what we assume to be Rose Hill. Chattanooga, TN, is in extreme southeast Tennessee, the complete opposite corner of the state.
When Happy is in the ICU the nurse adjusts the roller clamp to the IV fluid. A pump controls the flow-adjusting the roller clamp would do nothing except shut off the medication, causing the machine to call for attention.
When Tony is zip-tied to the bed, he asks one of the guards the distance between Miami and Tennessee. The guard says 832 miles, which is correct for some parts of Tennessee. This means Tony's armor is ~832 miles away. Even assuming his armor travels at 1000 miles/hour, it would take his armor almost an hour to get to him, rather than the few minutes shown in the movie. Tony's armor would have to travel at almost 10,000 miles/hour to get to Tony in 5 minutes. The current airspeed record for a plane is only 2,193 miles/hour. Tony's armor, at the current airspeed record, would still take 23 minutes to get to him.