When Tony Stark is showing Yinsen the schematic for the Iron Man suit, the newly made mini arc reactor is glowing in his shirt. Then in the next scene it shows them placing the one in he just made before that scene.
(at around 8 mins) When Tony Stark is being interviewed by Christine Everhart, his goatee is small, thin, and pointed, and his mustache appears almost drawn-on. The following morning, after seducing her, his goatee and mustache have grown, becoming round and full, in far too little time to be natural.
(at around 1h 7 mins) When Tony Stark drives his Audi R8 to Disney Hall for the benefit event, there is no front license plate affixed to the vehicle. However, when he pulls up to the entrance, his "STARK4" vanity plate is clearly visible on the front of the car.
(at around 1h 5 mins) While Stark is working on the flight stabilizers, Pepper brings down a box with a cup of coffee on top of it. Following that, Stark eventually goes upstairs, talks with Stane, comes back down, finishes the stabilizers, tests them, builds the entire prototype suit, test flies it, returns and picks the coffee up off the top of the box. Steam can be seen coming off the cup even though it's probably hours, if not days, old.
(at around 1h 12 mins) When Tony Stark is buying a drink, he puts a folded bill in the tip glass, which can be seen sticking out from the rest. When it cuts to a close-up of the money glass, Tony's tip is no longer there.
(at around 1h 23 mins) Stark falls off of one plane and another plane flies through him shearing off its left wing. The plane immediately starts a clockwise roll as if the right wing's weight would cause the right side of the plane to dip. In actuality the plane would roll counter clockwise because the only lift is from the right wing so it would rise.
(at around 1h 24 mins) When Rhodey holds the news conference announcing the unfortunate training exercise, his rank broadcast on Channel 3 KNKV News on-screen is "Col. James Rhodes". Verbally addressing him as Colonel Rhodes would be acceptable, but protocol would dictate his rank be displayed as "Lt Col" (Lieutenant Colonel).
(at around 24 mins) Molten palladium is incandescent (about 1550°C), glowing yellow-white if not white-hot. The palladium that Yinsen pours is nowhere near that temperature; it is not even at red heat.
(at around 4 mins) Newspaper clipping dated Friday December 17 1991, during the award ceremony telling about Stark's parents' death. However, December 17 1991 was a Tuesday.
(at around 3 mins) A rocket is seen burrowing into the dirt next to Tony before exploding. The warhead is clearly blue and likely a Mk 153 SMAW round. Any munition in use with the military that is blue (such as the SMAW Common Practice Round) is used for the sole purpose of training and would therefore not explode.
(at around 43 mins) Outside the press conference, Tony pulls one Burger King cheeseburger out of the bag Hogan is holding and is seen finishing it in the next scene when he is walking to the podium. But, when Tony is seated and begins talking about his father, he pulls the cheeseburger out of his pocket and begins eating it. When Stane asked if he had one for him, Stark replied that there was only one left, suggesting he bought more than one.
In fact, he did buy more than one burger as he was finishing one when he was getting out of the car. There is a good chance that he placed one in his coat pocket before reaching for the last one in the bag. When Stane asked him if he had one for him he had one open in his hand getting ready to eat it and one in his pocket for eating later.
(at around 25 mins) When Yinsen asks Tony Stark about the first arc discharge reactors capacity, Stark gives it in gigajoules per second. From this Yinsen calculates that it could sustain his heart for fifty lifetimes. This deduction is impossible, as total running time of a device requires knowledge of total energy produced and not just instantaneous power which Joules per second describes. However, this is not a goof, as Yinsen may have seen some calculations of Stark's and with this new information, reached his conclusion.
The Afghan people speak in Arabic which is wrong. In fact, Afghan people speak in Ordu, Pashtu and Farsi, not Arabic.
However, Yinsen tells Tony that the group that captures him speak many different languages.
When Tony reveals the power generation of the first arc reactor he uses in his chest, he gives it in gigajoules per second (more typically called gigawatts). Since the reactor is generating this much power, the amount of power available to the suit in the ending battle should not be dropping steadily, but should be constant until the reactor stops generating power. However, given the high amount of advanced technology all constantly being run at the same time while the suit is operational, it's entirely plausible that the suit is using more energy per second than the reactor is generating, resulting in a steady loss of total power available and causing him to switch to the backup power source while the reactor catches back up.
While Rhodes is a Lieutenant Colonel (officer rank 5), he is referred to as "Colonel Rhodes" through out the movie. It is common for Lieutenant Colonels to be referred to as Colonel. The same is true for Lieutenant Commanders, and the various ranks of Generals and Admirals to be called the shortened form of their rank.
Tony's mustache alternates between a real mustache and an applied prosthetic, throughout the film.
(at around 1h 6 mins) Several of the devices in Tony's home display live transcriptions of what Tony says. In some cases, the transcript appears slightly before Tony says the words.
(at around 50 mins) When Stark is lying on the table and asking Pepper to remove the power cell from his chest, the prosthetic chest used for the effect is moving up and down to simulate his breathing. Tony's actual breathing is out of sync with that of the prosthetic chest.
(at around 1h 11 mins) At the benefit party, when Tony Stark gets the two Martinis at the bar, the girl to his right looks into the camera for an instant.
(at around 1h 18 mins) When the tank shoots at Tony and he dodges the projectile, there is no explosion or sound of it hitting the wall, the ground, or anything behind him.
When Stark is found in the dessert by Rhodes, his military personnel are pointing their guns towards Stark like as if he was a threat instead of securing the perimeter.
(at around 15 mins) When the "Jericho" rocket explodes in the distance, an explosion is heard, this is not possible due to the speed of sound being much slower than the speed of light.
(at around 1h 6 mins) When Tony is upgrading the MkII suit to correct the icing problem, one of the screens behind him is taking a real-time transcript of his and JARVIS's dialogue. When JARVIS asks "Shall I render using proposed specifications?", the computer screen says "utilizing" instead of "using."
(at around 11 mins) When Pepper comes down the stairs to see Tony working on his motorcycle as the glass door closes behind her, a staff worker is visible in the reflection of the door.
(at around 21 mins) Crew are visible in the reflection of Yinsen's glasses outside of the cave when Tony "agrees" to create the Jericho missile.
(around 30 minutes) When Yinsen is lying on the grain bags, the fill light and the shadow of the boom mic are visible in his glasses.
(at around 43 mins) Reflected on the windshield of the car, as Obadiah greets Tony at his press conference after escaping from captivity.
(at around 4 mins) Stark is said to have graduated from MIT summa cum laude, but MIT does not graduate people with honors.
Rhodes wears his MIT class ring (the Brass Rat) backwards, with the rat (really a beaver) facing him. Undergraduates wear the ring facing them. After graduation, they turn the ring around.
During the F22 Raptor scene, Rhodes orders the Major to stop the attack. The Major aggressively overrules him, this would be insubordinate since Rhodes outranks him as a Lt. Colonel.
Tony Stark is shown learning to control the powerful thrusters in the suits hands and feet. It takes Tony considerable time to master the art of flying. However, when Stane acquires the arc reactor from Tony and inserts it into his new iron suit, he is able to fly and maneuver well, immediately.
(at around 1h 22 mins) When the F-22's are shooting at Iron Man, Rhodes and the "Major" are wearing headsets that have a mic; they are wearing them over the top of their heads, with parts of them pressing on their ears. These headsets are meant to go around the back of the head with the curved part going over each ear. These headsets are actually only a microphone, and no sounds is piped to the headset.