The Rock Goofs
Factual Errors: VX is a nerve agent and does not melt skin.
Factual Errors: When atropine is used an antidote to nerve gas, it is usually injected into the thigh via a spring-loaded syringe. It is not recommended (and far more difficult) for non-medical personnel to inject it into the heart with a conventional syringe.
Factual Errors: The scientists outside the gas chamber shout at the men inside to inject themselves "before your suits melt." Atropine is toxic if taken when exposure to a nerve agent has not actually taken place - taking it before the suits have melted would incapacitate the agents. Furthermore, anyone who had been injected with atropine (whether before or after nerve agent exposure) would be in no fit state to either defuse a bomb or, as Goodspeed does at the end of the film, get up and run outside to light the flares.
Continuity: The windshield of the Humvee after smashing through the water bottle truck.
Continuity: The windshield of the Ferrari after crashing into the parking meters.
Continuity: When the Humvee crashes into the meter-maid vehicle, it skids and goes sideways. In the next shot, it is still pointed straight down the street.
Continuity: The wheel on the motorcycle that Goodspeed is riding can be seen stationary momentarily.
Factual Errors: Airbags deflate in well under a second and hence would not obstruct a driver's view of the road as indicated.
Continuity: In the helicopter on the way to Alcatraz, Lt. Shepard quickly loses the headset he is seen to be putting on.
Continuity: Mason and Stanley dry off too quickly after sheltering underwater from the firebombs.
Continuity: The first lever that Mason flicks from his cell resets itself before he activates the second one.
Continuity: Mason and Goodspeed peer through a slot in the wall that is open when Goodspeed looks at it, but closed when he motions for Mason to look.
Continuity: The plane which rolls out of the hanger is a two seater F/A-18 Hornet, yet all aircraft in the flight squadron are single seaters.
Factual Errors: The aircraft used to drop the thermite plasma are F/A-18s, which are normally US Navy jets, but they have US Air Force markings as do the pilots flying them. The Air Force flies F-16s.
Errors in geography: Final scene obviously not filmed in Kansas.
Incorrectly regarded as goofs: How can Mason be imprisoned in Alcatraz in 1962 for stealing files about the Kennedy Assassination (November 1963)? Easily: the film supports the rumour that Kennedy was assassinated by a government agency, and there existed confidential documents in 1962 about the upcoming assassination.
Incorrectly regarded as goofs: When entering Alcatraz, Mason jumps through wheels and flames to get into the building. He said he had to learn the sequences when he escaped in the 60s. But as soon he's inside Alcatraz he opens a door from the inside. Why didn't he escape through this door in the 1960? Because in the 1960s, when Alcatraz was a prison, that door was locked.
Incorrectly regarded as goofs: It appears that Goodspeed leaps to catch the rolling VX in his right hand, catches it in his left, then has it in his right again, but close examination reveals he quickly pushes the ball from one hand to the other.
Factual Errors: When Mason throws Wormack over the balcony of the hotel he does so using a clothesline rope (probably nylon) in a slip knot around his wrist. With the combination of his body weight and the velocity of the fall such a rope should slice straight through Wormack's wrist and he would plunge to his death.
Continuity: The number of F-18s headed toward Alcatraz varies between four, five and six.
Incorrectly regarded as goofs: Mason has been imprisoned for the past 30 years yet when he escapes he knows how to work a cell phone (reasonable, since it's not hard) and modern scuba gear (which hasn't changed all that much).
Incorrectly regarded as goofs: Mason was captured and locked away in 1962, but has a daughter born after 1972. That's because, as we learn, he escaped before, and presumably sowed some wild oats during one of those episodes.
Continuity: At the end of the movie Mason says its been a long time since he's thanked anyone for anything. However, the day before he thanked Goodspeed for not embarrassing him in front of his daughter.
Plot holes: At the end Goodspeed puts a glass sphere in the pocket on his chest. We do not see any measures taken to prevent it from breaking. But in the fight afterward we clearly see Goodspeed land on his chest. The same glass later breaks quite easily in the mouth of the terrorist.
Crew or equipment visible: Supporting cables visible on the first camera shot of Goodspeed being blown into the sea.
Revealing mistakes: General Hummel clearly lands on a mat after he is shot.
Crew or equipment visible: Cameras are visible on the roads at several points during the car chase (Mason's Humvee can be seen to drive over one as it collides with the vehicles by the telegraph pole).
Revealing mistakes: During the chase scene with the Humvee, one of the cars that flips, clearly showing the explosives-holding special effects canister under the car, still smoking.
Revealing mistakes: When the cable car is knocked off its tracks, slides down the hill and explodes, you can see the road behind and there are no tracks coming down the hill.
Continuity: The old lady seen crossing in front of the crashing trolley is also a passenger on the same trolley.
Factual Errors: Hummel tells General Kramer that the government has 40 hours to pay the $100 million. However, his second call is at 0000, and in the same call to General Kramer, Hummal says that the deadline is "midday tomorrow" - which of course is only 36 hours later, not 40.
Continuity: While talking to his daughter in the Palace of Fine Arts, Mason's tie changes.
Continuity: The tether rope on the morgue cart disappears and reappears.
Continuity: The same extras (most notably the man with a large white beard) can be seen standing both on the left and on the right of the Ferrari when it breaks the storefront window.
Crew or equipment visible: When the planes drop the thermite plasma, Goodspeed is launched into the air and you can clearly see the cable holding him.
Continuity: The tour guide's socks are up/down between shots in the prison.
Miscellaneous: Captain Frye tells Hummel to "be all that we can be". This is the former slogan of the US Army, not the 
Navy...