Continuity mistake: At the end of the movie just after Senator Stern pins medals on James Rhodes and Tony Stark, we see a shot where Tony puts his arm around the Senator. All three men are arm in arm. The camera angle changes to the back of the men, and Tony's arm is at his side. Then when the camera angle goes back to the front of the three men, Tony's arm is back around the Senator. (01:56:07 - 01:56:57)
Other mistake: When Tony goes to the bathroom and scans his blood toxicity, the Tony who faces the camera is supposed to be his reflection in the mirror, but oddly the problem is the reflection is not actually reversed. And note how he scanned his right hand's finger, but then he's sucking on his left hand's pricked finger. (00:28:30)
Continuity mistake: At the end of the movie where Stark, Rhody and the Senator are taking a photo, Stark's hand is supposed to be behind the senator but when the scene switches to the zoomed out view, his hands are by his side and when it switches back again, his hands are behind the senator.
Continuity mistake: When Ivan climbs the ladder to inspect the Hammer prototype, his hair changes repeatedly from underneath the frames of his glasses to outside the frames. (00:51:00)
Continuity mistake: The scene in the Monaco lounge when Tony Stark and Justin Hammer are sitting down at a table with Christine Everhart to give an interview, Hammer sets his drink on the table while he's standing but then the shot immediately cuts to him sitting down with the drink still in his hand.
Continuity mistake: Before Hammer starts eating dessert (and thus much before the "moving spoon and cherry" continuity mistakes), there's a back angle where he dips his spoon into the dessert and starts eating. The angle cuts to a front view with the spoon laying spotless on the saucer, and Hammer saying "I'll start with dessert", and then repeating the whole previous scene as if it were the first time.
Continuity mistake: In the beginning when Tony's press conference is on TV in Anton Vanko's home, the dialogue exchange between Tony and Christine Everheart has more talking than that same scene in "Iron Man" at the end. In "2", Christine mentions that Tony hates body guards in the exchange, but, this is never said in the first "Iron Man".